[{"data":1,"prerenderedAt":2859},["ShallowReactive",2],{"blog-\u002Fblog\u002Fdip-and-strike-geological-surveying":3,"blog-surround-\u002Fblog\u002Fdip-and-strike-geological-surveying":2848},{"id":4,"title":5,"author":6,"body":7,"category":2817,"description":2818,"extension":2819,"image":2820,"meta":2821,"navigation":2840,"path":2841,"publishedAt":2842,"readTime":2843,"seo":2844,"sitemap":2845,"stem":2846,"__hash__":2847},"blog\u002Fblog\u002F26.dip-and-strike-geological-surveying.md","Dip and Strike: Mastering Sloping Planes in Earthworks","Surveyiiing Expert",{"type":8,"value":9,"toc":2797},"minimark",[10,15,28,32,151,155,444,448,703,2299,2303,2375,2379,2643,2647,2695,2699,2721,2725,2786,2790],[11,12,14],"h2",{"id":13},"overview","Overview",[16,17,18,19,23,24,27],"p",{},"In earthworks and geological engineering, we often deal with tilted planes—such as rock strata or sloping site excavations. To define these planes mathematically, surveyors use the concepts of ",[20,21,22],"strong",{},"Dip"," and ",[20,25,26],{},"Strike",". Understanding these is essential for predicting the depth of rock layers or designing the intersection of different site slopes .",[11,29,31],{"id":30},"theory","Theory",[33,34,35,42,145],"ul",{},[36,37,38,41],"li",{},[20,39,40],{},"Full Dip:"," The direction of maximum tilt on a plane .",[36,43,44,47,48,144],{},[20,45,46],{},"Strike Line:"," A level line on the plane, which is always at right angles (",[49,50,53,83],"span",{"className":51},[52],"katex",[49,54,57],{"className":55},[56],"katex-mathml",[58,59,61],"math",{"xmlns":60},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[62,63,64,78],"semantics",{},[65,66,67],"mrow",{},[68,69,70,74],"msup",{},[71,72,73],"mn",{},"90",[75,76,77],"mo",{},"∘",[79,80,82],"annotation",{"encoding":81},"application\u002Fx-tex","90^\\circ",[49,84,88],{"className":85,"ariaHidden":87},[86],"katex-html","true",[49,89,92,97,102],{"className":90},[91],"base",[49,93],{"className":94,"style":96},[95],"strut","height:0.6741em;",[49,98,101],{"className":99},[100],"mord","9",[49,103,105,109],{"className":104},[100],[49,106,108],{"className":107},[100],"0",[49,110,113],{"className":111},[112],"msupsub",[49,114,117],{"className":115},[116],"vlist-t",[49,118,121],{"className":119},[120],"vlist-r",[49,122,125],{"className":123,"style":96},[124],"vlist",[49,126,128,133],{"style":127},"top:-3.063em;margin-right:0.05em;",[49,129],{"className":130,"style":132},[131],"pstrut","height:2.7em;",[49,134,140],{"className":135},[136,137,138,139],"sizing","reset-size6","size3","mtight",[49,141,77],{"className":142},[143,139],"mbin",") to the direction of full dip .",[36,146,147,150],{},[20,148,149],{},"Apparent Dip:"," Any grade on the plane measured in a direction other than full dip. An apparent dip is always less steep than the full dip .",[11,152,154],{"id":153},"mathematical-principles","Mathematical Principles",[16,156,157,158,192,193,272,273,304,305],{},"The fundamental relationship between full dip (",[49,159,161,177],{"className":160},[52],[49,162,164],{"className":163},[56],[58,165,166],{"xmlns":60},[62,167,168,174],{},[65,169,170],{},[171,172,173],"mi",{},"θ",[79,175,176],{"encoding":81},"\\theta",[49,178,180],{"className":179,"ariaHidden":87},[86],[49,181,183,187],{"className":182},[91],[49,184],{"className":185,"style":186},[95],"height:0.6944em;",[49,188,173],{"className":189,"style":191},[100,190],"mathnormal","margin-right:0.0278em;",") and an apparent dip (",[49,194,196,216],{"className":195},[52],[49,197,199],{"className":198},[56],[58,200,201],{"xmlns":60},[62,202,203,213],{},[65,204,205],{},[206,207,208,210],"msub",{},[171,209,173],{},[71,211,212],{},"1",[79,214,215],{"encoding":81},"\\theta_1",[49,217,219],{"className":218,"ariaHidden":87},[86],[49,220,222,226],{"className":221},[91],[49,223],{"className":224,"style":225},[95],"height:0.8444em;vertical-align:-0.15em;",[49,227,229,232],{"className":228},[100],[49,230,173],{"className":231,"style":191},[100,190],[49,233,235],{"className":234},[112],[49,236,239,263],{"className":237},[116,238],"vlist-t2",[49,240,242,258],{"className":241},[120],[49,243,246],{"className":244,"style":245},[124],"height:0.3011em;",[49,247,249,252],{"style":248},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[49,250],{"className":251,"style":132},[131],[49,253,255],{"className":254},[136,137,138,139],[49,256,212],{"className":257},[100,139],[49,259,262],{"className":260},[261],"vlist-s","​",[49,264,266],{"className":265},[120],[49,267,270],{"className":268,"style":269},[124],"height:0.15em;",[49,271],{},") measured at an angle ",[49,274,276,291],{"className":275},[52],[49,277,279],{"className":278},[56],[58,280,281],{"xmlns":60},[62,282,283,288],{},[65,284,285],{},[171,286,287],{},"ϕ",[79,289,290],{"encoding":81},"\\phi",[49,292,294],{"className":293,"ariaHidden":87},[86],[49,295,297,301],{"className":296},[91],[49,298],{"className":299,"style":300},[95],"height:0.8889em;vertical-align:-0.1944em;",[49,302,287],{"className":303},[100,190]," to the full dip direction is:\n",[49,306,308,348],{"className":307},[52],[49,309,311],{"className":310},[56],[58,312,313],{"xmlns":60},[62,314,315,345],{},[65,316,317,320,323,329,332,334,336,338,341,343],{},[171,318,319],{},"tan",[75,321,322],{},"⁡",[206,324,325,327],{},[171,326,173],{},[71,328,212],{},[75,330,331],{},"=",[171,333,319],{},[75,335,322],{},[171,337,173],{},[171,339,340],{},"cos",[75,342,322],{},[171,344,287],{},[79,346,347],{"encoding":81},"\\tan \\theta_1 = \\tan \\theta \\cos \\phi",[49,349,351,417],{"className":350,"ariaHidden":87},[86],[49,352,354,357,361,366,406,410,414],{"className":353},[91],[49,355],{"className":356,"style":225},[95],[49,358,319],{"className":359},[360],"mop",[49,362],{"className":363,"style":365},[364],"mspace","margin-right:0.1667em;",[49,367,369,372],{"className":368},[100],[49,370,173],{"className":371,"style":191},[100,190],[49,373,375],{"className":374},[112],[49,376,378,398],{"className":377},[116,238],[49,379,381,395],{"className":380},[120],[49,382,384],{"className":383,"style":245},[124],[49,385,386,389],{"style":248},[49,387],{"className":388,"style":132},[131],[49,390,392],{"className":391},[136,137,138,139],[49,393,212],{"className":394},[100,139],[49,396,262],{"className":397},[261],[49,399,401],{"className":400},[120],[49,402,404],{"className":403,"style":269},[124],[49,405],{},[49,407],{"className":408,"style":409},[364],"margin-right:0.2778em;",[49,411,331],{"className":412},[413],"mrel",[49,415],{"className":416,"style":409},[364],[49,418,420,423,426,429,432,435,438,441],{"className":419},[91],[49,421],{"className":422,"style":300},[95],[49,424,319],{"className":425},[360],[49,427],{"className":428,"style":365},[364],[49,430,173],{"className":431,"style":191},[100,190],[49,433],{"className":434,"style":365},[364],[49,436,340],{"className":437},[360],[49,439],{"className":440,"style":365},[364],[49,442,287],{"className":443},[100,190],[11,445,447],{"id":446},"step-by-step-example","Step-by-Step Example",[16,449,450,453,454,483,484,513,514,578,579,644,645,483,673,702],{},[20,451,452],{},"Problem:"," On a stratum plane, an apparent dip of ",[49,455,457,470],{"className":456},[52],[49,458,460],{"className":459},[56],[58,461,462],{"xmlns":60},[62,463,464,468],{},[65,465,466],{},[71,467,212],{},[79,469,212],{"encoding":81},[49,471,473],{"className":472,"ariaHidden":87},[86],[49,474,476,480],{"className":475},[91],[49,477],{"className":478,"style":479},[95],"height:0.6444em;",[49,481,212],{"className":482},[100]," in ",[49,485,487,501],{"className":486},[52],[49,488,490],{"className":489},[56],[58,491,492],{"xmlns":60},[62,493,494,499],{},[65,495,496],{},[71,497,498],{},"16",[79,500,498],{"encoding":81},[49,502,504],{"className":503,"ariaHidden":87},[86],[49,505,507,510],{"className":506},[91],[49,508],{"className":509,"style":479},[95],[49,511,498],{"className":512},[100]," bears ",[49,515,517,536],{"className":516},[52],[49,518,520],{"className":519},[56],[58,521,522],{"xmlns":60},[62,523,524,533],{},[65,525,526],{},[68,527,528,531],{},[71,529,530],{},"170",[75,532,77],{},[79,534,535],{"encoding":81},"170^\\circ",[49,537,539],{"className":538,"ariaHidden":87},[86],[49,540,542,545,549],{"className":541},[91],[49,543],{"className":544,"style":96},[95],[49,546,548],{"className":547},[100],"17",[49,550,552,555],{"className":551},[100],[49,553,108],{"className":554},[100],[49,556,558],{"className":557},[112],[49,559,561],{"className":560},[116],[49,562,564],{"className":563},[120],[49,565,567],{"className":566,"style":96},[124],[49,568,569,572],{"style":127},[49,570],{"className":571,"style":132},[131],[49,573,575],{"className":574},[136,137,138,139],[49,576,77],{"className":577},[143,139],", and another apparent dip in the direction ",[49,580,582,601],{"className":581},[52],[49,583,585],{"className":584},[56],[58,586,587],{"xmlns":60},[62,588,589,598],{},[65,590,591],{},[68,592,593,596],{},[71,594,595],{},"194",[75,597,77],{},[79,599,600],{"encoding":81},"194^\\circ",[49,602,604],{"className":603,"ariaHidden":87},[86],[49,605,607,610,614],{"className":606},[91],[49,608],{"className":609,"style":96},[95],[49,611,613],{"className":612},[100],"19",[49,615,617,621],{"className":616},[100],[49,618,620],{"className":619},[100],"4",[49,622,624],{"className":623},[112],[49,625,627],{"className":626},[116],[49,628,630],{"className":629},[120],[49,631,633],{"className":632,"style":96},[124],[49,634,635,638],{"style":127},[49,636],{"className":637,"style":132},[131],[49,639,641],{"className":640},[136,137,138,139],[49,642,77],{"className":643},[143,139]," is ",[49,646,648,661],{"className":647},[52],[49,649,651],{"className":650},[56],[58,652,653],{"xmlns":60},[62,654,655,659],{},[65,656,657],{},[71,658,212],{},[79,660,212],{"encoding":81},[49,662,664],{"className":663,"ariaHidden":87},[86],[49,665,667,670],{"className":666},[91],[49,668],{"className":669,"style":479},[95],[49,671,212],{"className":672},[100],[49,674,676,690],{"className":675},[52],[49,677,679],{"className":678},[56],[58,680,681],{"xmlns":60},[62,682,683,688],{},[65,684,685],{},[71,686,687],{},"11",[79,689,687],{"encoding":81},[49,691,693],{"className":692,"ariaHidden":87},[86],[49,694,696,699],{"className":695},[91],[49,697],{"className":698,"style":479},[95],[49,700,687],{"className":701},[100],". Calculate the direction and rate of full dip .",[704,705,706,1185,1402,1921],"ol",{},[36,707,708,711,712,743,744,972],{},[20,709,710],{},"Set up equations:","\nLet full dip direction be ",[49,713,715,730],{"className":714},[52],[49,716,718],{"className":717},[56],[58,719,720],{"xmlns":60},[62,721,722,727],{},[65,723,724],{},[171,725,726],{},"δ",[79,728,729],{"encoding":81},"\\delta",[49,731,733],{"className":732,"ariaHidden":87},[86],[49,734,736,739],{"className":735},[91],[49,737],{"className":738,"style":186},[95],[49,740,726],{"className":741,"style":742},[100,190],"margin-right:0.0379em;",".\n",[49,745,747,804],{"className":746},[52],[49,748,750],{"className":749},[56],[58,751,752],{"xmlns":60},[62,753,754,801],{},[65,755,756,758,760,767,769,771,773,776,779,781,783,787,793,796,798],{},[171,757,319],{},[75,759,322],{},[206,761,762,765],{},[763,764,22],"mtext",{},[71,766,212],{},[75,768,331],{},[171,770,319],{},[75,772,322],{},[763,774,775],{},"Full Dip",[75,777,778],{},"×",[171,780,340],{},[75,782,322],{},[75,784,786],{"stretchy":785},"false","(",[68,788,789,791],{},[71,790,530],{},[75,792,77],{},[75,794,795],{},"−",[171,797,726],{},[75,799,800],{"stretchy":785},")",[79,802,803],{"encoding":81},"\\tan \\text{Dip}_1 = \\tan \\text{Full Dip} \\times \\cos(170^\\circ - \\delta)",[49,805,807,876,904,959],{"className":806,"ariaHidden":87},[86],[49,808,810,814,817,820,867,870,873],{"className":809},[91],[49,811],{"className":812,"style":813},[95],"height:0.9275em;vertical-align:-0.2441em;",[49,815,319],{"className":816},[360],[49,818],{"className":819,"style":365},[364],[49,821,823,830],{"className":822},[100],[49,824,827],{"className":825},[100,826],"text",[49,828,22],{"className":829},[100],[49,831,833],{"className":832},[112],[49,834,836,858],{"className":835},[116,238],[49,837,839,855],{"className":838},[120],[49,840,843],{"className":841,"style":842},[124],"height:0.207em;",[49,844,846,849],{"style":845},"top:-2.4559em;margin-right:0.05em;",[49,847],{"className":848,"style":132},[131],[49,850,852],{"className":851},[136,137,138,139],[49,853,212],{"className":854},[100,139],[49,856,262],{"className":857},[261],[49,859,861],{"className":860},[120],[49,862,865],{"className":863,"style":864},[124],"height:0.2441em;",[49,866],{},[49,868],{"className":869,"style":409},[364],[49,871,331],{"className":872},[413],[49,874],{"className":875,"style":409},[364],[49,877,879,882,885,888,894,898,901],{"className":878},[91],[49,880],{"className":881,"style":300},[95],[49,883,319],{"className":884},[360],[49,886],{"className":887,"style":365},[364],[49,889,891],{"className":890},[100,826],[49,892,775],{"className":893},[100],[49,895],{"className":896,"style":897},[364],"margin-right:0.2222em;",[49,899,778],{"className":900},[143],[49,902],{"className":903,"style":897},[364],[49,905,907,911,914,918,921,950,953,956],{"className":906},[91],[49,908],{"className":909,"style":910},[95],"height:1em;vertical-align:-0.25em;",[49,912,340],{"className":913},[360],[49,915,786],{"className":916},[917],"mopen",[49,919,548],{"className":920},[100],[49,922,924,927],{"className":923},[100],[49,925,108],{"className":926},[100],[49,928,930],{"className":929},[112],[49,931,933],{"className":932},[116],[49,934,936],{"className":935},[120],[49,937,939],{"className":938,"style":96},[124],[49,940,941,944],{"style":127},[49,942],{"className":943,"style":132},[131],[49,945,947],{"className":946},[136,137,138,139],[49,948,77],{"className":949},[143,139],[49,951],{"className":952,"style":897},[364],[49,954,795],{"className":955},[143],[49,957],{"className":958,"style":897},[364],[49,960,962,965,968],{"className":961},[91],[49,963],{"className":964,"style":910},[95],[49,966,726],{"className":967,"style":742},[100,190],[49,969,800],{"className":970},[971],"mclose",[49,973,975,1026],{"className":974},[52],[49,976,978],{"className":977},[56],[58,979,980],{"xmlns":60},[62,981,982,1023],{},[65,983,984,986,988,995,997,999,1001,1003,1005,1007,1009,1011,1017,1019,1021],{},[171,985,319],{},[75,987,322],{},[206,989,990,992],{},[763,991,22],{},[71,993,994],{},"2",[75,996,331],{},[171,998,319],{},[75,1000,322],{},[763,1002,775],{},[75,1004,778],{},[171,1006,340],{},[75,1008,322],{},[75,1010,786],{"stretchy":785},[68,1012,1013,1015],{},[71,1014,595],{},[75,1016,77],{},[75,1018,795],{},[171,1020,726],{},[75,1022,800],{"stretchy":785},[79,1024,1025],{"encoding":81},"\\tan \\text{Dip}_2 = \\tan \\text{Full Dip} \\times \\cos(194^\\circ - \\delta)",[49,1027,1029,1093,1120,1173],{"className":1028,"ariaHidden":87},[86],[49,1030,1032,1035,1038,1041,1084,1087,1090],{"className":1031},[91],[49,1033],{"className":1034,"style":813},[95],[49,1036,319],{"className":1037},[360],[49,1039],{"className":1040,"style":365},[364],[49,1042,1044,1050],{"className":1043},[100],[49,1045,1047],{"className":1046},[100,826],[49,1048,22],{"className":1049},[100],[49,1051,1053],{"className":1052},[112],[49,1054,1056,1076],{"className":1055},[116,238],[49,1057,1059,1073],{"className":1058},[120],[49,1060,1062],{"className":1061,"style":842},[124],[49,1063,1064,1067],{"style":845},[49,1065],{"className":1066,"style":132},[131],[49,1068,1070],{"className":1069},[136,137,138,139],[49,1071,994],{"className":1072},[100,139],[49,1074,262],{"className":1075},[261],[49,1077,1079],{"className":1078},[120],[49,1080,1082],{"className":1081,"style":864},[124],[49,1083],{},[49,1085],{"className":1086,"style":409},[364],[49,1088,331],{"className":1089},[413],[49,1091],{"className":1092,"style":409},[364],[49,1094,1096,1099,1102,1105,1111,1114,1117],{"className":1095},[91],[49,1097],{"className":1098,"style":300},[95],[49,1100,319],{"className":1101},[360],[49,1103],{"className":1104,"style":365},[364],[49,1106,1108],{"className":1107},[100,826],[49,1109,775],{"className":1110},[100],[49,1112],{"className":1113,"style":897},[364],[49,1115,778],{"className":1116},[143],[49,1118],{"className":1119,"style":897},[364],[49,1121,1123,1126,1129,1132,1135,1164,1167,1170],{"className":1122},[91],[49,1124],{"className":1125,"style":910},[95],[49,1127,340],{"className":1128},[360],[49,1130,786],{"className":1131},[917],[49,1133,613],{"className":1134},[100],[49,1136,1138,1141],{"className":1137},[100],[49,1139,620],{"className":1140},[100],[49,1142,1144],{"className":1143},[112],[49,1145,1147],{"className":1146},[116],[49,1148,1150],{"className":1149},[120],[49,1151,1153],{"className":1152,"style":96},[124],[49,1154,1155,1158],{"style":127},[49,1156],{"className":1157,"style":132},[131],[49,1159,1161],{"className":1160},[136,137,138,139],[49,1162,77],{"className":1163},[143,139],[49,1165],{"className":1166,"style":897},[364],[49,1168,795],{"className":1169},[143],[49,1171],{"className":1172,"style":897},[364],[49,1174,1176,1179,1182],{"className":1175},[91],[49,1177],{"className":1178,"style":910},[95],[49,1180,726],{"className":1181,"style":742},[100,190],[49,1183,800],{"className":1184},[971],[36,1186,1187,1190,1401],{},[20,1188,1189],{},"Equate through Full Dip:",[49,1191,1193,1247],{"className":1192},[52],[49,1194,1196],{"className":1195},[56],[58,1197,1198],{"xmlns":60},[62,1199,1200,1244],{},[65,1201,1202,1204,1206,1208,1210,1216,1218,1220,1222,1224,1226,1228,1230,1232,1238,1240,1242],{},[71,1203,498],{},[171,1205,340],{},[75,1207,322],{},[75,1209,786],{"stretchy":785},[68,1211,1212,1214],{},[71,1213,530],{},[75,1215,77],{},[75,1217,795],{},[171,1219,726],{},[75,1221,800],{"stretchy":785},[75,1223,331],{},[71,1225,687],{},[171,1227,340],{},[75,1229,322],{},[75,1231,786],{"stretchy":785},[68,1233,1234,1236],{},[71,1235,595],{},[75,1237,77],{},[75,1239,795],{},[171,1241,726],{},[75,1243,800],{"stretchy":785},[79,1245,1246],{"encoding":81},"16 \\cos(170^\\circ - \\delta) = 11 \\cos(194^\\circ - \\delta)",[49,1248,1250,1309,1330,1389],{"className":1249,"ariaHidden":87},[86],[49,1251,1253,1256,1259,1262,1265,1268,1271,1300,1303,1306],{"className":1252},[91],[49,1254],{"className":1255,"style":910},[95],[49,1257,498],{"className":1258},[100],[49,1260],{"className":1261,"style":365},[364],[49,1263,340],{"className":1264},[360],[49,1266,786],{"className":1267},[917],[49,1269,548],{"className":1270},[100],[49,1272,1274,1277],{"className":1273},[100],[49,1275,108],{"className":1276},[100],[49,1278,1280],{"className":1279},[112],[49,1281,1283],{"className":1282},[116],[49,1284,1286],{"className":1285},[120],[49,1287,1289],{"className":1288,"style":96},[124],[49,1290,1291,1294],{"style":127},[49,1292],{"className":1293,"style":132},[131],[49,1295,1297],{"className":1296},[136,137,138,139],[49,1298,77],{"className":1299},[143,139],[49,1301],{"className":1302,"style":897},[364],[49,1304,795],{"className":1305},[143],[49,1307],{"className":1308,"style":897},[364],[49,1310,1312,1315,1318,1321,1324,1327],{"className":1311},[91],[49,1313],{"className":1314,"style":910},[95],[49,1316,726],{"className":1317,"style":742},[100,190],[49,1319,800],{"className":1320},[971],[49,1322],{"className":1323,"style":409},[364],[49,1325,331],{"className":1326},[413],[49,1328],{"className":1329,"style":409},[364],[49,1331,1333,1336,1339,1342,1345,1348,1351,1380,1383,1386],{"className":1332},[91],[49,1334],{"className":1335,"style":910},[95],[49,1337,687],{"className":1338},[100],[49,1340],{"className":1341,"style":365},[364],[49,1343,340],{"className":1344},[360],[49,1346,786],{"className":1347},[917],[49,1349,613],{"className":1350},[100],[49,1352,1354,1357],{"className":1353},[100],[49,1355,620],{"className":1356},[100],[49,1358,1360],{"className":1359},[112],[49,1361,1363],{"className":1362},[116],[49,1364,1366],{"className":1365},[120],[49,1367,1369],{"className":1368,"style":96},[124],[49,1370,1371,1374],{"style":127},[49,1372],{"className":1373,"style":132},[131],[49,1375,1377],{"className":1376},[136,137,138,139],[49,1378,77],{"className":1379},[143,139],[49,1381],{"className":1382,"style":897},[364],[49,1384,795],{"className":1385},[143],[49,1387],{"className":1388,"style":897},[364],[49,1390,1392,1395,1398],{"className":1391},[91],[49,1393],{"className":1394,"style":910},[95],[49,1396,726],{"className":1397,"style":742},[100,190],[49,1399,800],{"className":1400},[971]," .",[36,1403,1404,1436,1437,1612,1613,1784,1785,1818,1819,1852,1853,1401],{},[20,1405,1406,1407,1435],{},"Solve for ",[49,1408,1410,1423],{"className":1409},[52],[49,1411,1413],{"className":1412},[56],[58,1414,1415],{"xmlns":60},[62,1416,1417,1421],{},[65,1418,1419],{},[171,1420,726],{},[79,1422,729],{"encoding":81},[49,1424,1426],{"className":1425,"ariaHidden":87},[86],[49,1427,1429,1432],{"className":1428},[91],[49,1430],{"className":1431,"style":186},[95],[49,1433,726],{"className":1434,"style":742},[100,190],":","\nUsing trigonometric expansion (",[49,1438,1440,1498],{"className":1439},[52],[49,1441,1443],{"className":1442},[56],[58,1444,1445],{"xmlns":60},[62,1446,1447,1495],{},[65,1448,1449,1451,1453,1455,1458,1460,1463,1465,1467,1469,1471,1473,1475,1477,1479,1482,1485,1487,1489,1491,1493],{},[171,1450,340],{},[75,1452,322],{},[75,1454,786],{"stretchy":785},[171,1456,1457],{},"A",[75,1459,795],{},[171,1461,1462],{},"B",[75,1464,800],{"stretchy":785},[75,1466,331],{},[171,1468,340],{},[75,1470,322],{},[171,1472,1457],{},[171,1474,340],{},[75,1476,322],{},[171,1478,1462],{},[75,1480,1481],{},"+",[171,1483,1484],{},"sin",[75,1486,322],{},[171,1488,1457],{},[171,1490,1484],{},[75,1492,322],{},[171,1494,1462],{},[79,1496,1497],{"encoding":81},"\\cos(A-B) = \\cos A \\cos B + \\sin A \\sin B",[49,1499,1501,1525,1547,1584],{"className":1500,"ariaHidden":87},[86],[49,1502,1504,1507,1510,1513,1516,1519,1522],{"className":1503},[91],[49,1505],{"className":1506,"style":910},[95],[49,1508,340],{"className":1509},[360],[49,1511,786],{"className":1512},[917],[49,1514,1457],{"className":1515},[100,190],[49,1517],{"className":1518,"style":897},[364],[49,1520,795],{"className":1521},[143],[49,1523],{"className":1524,"style":897},[364],[49,1526,1528,1531,1535,1538,1541,1544],{"className":1527},[91],[49,1529],{"className":1530,"style":910},[95],[49,1532,1462],{"className":1533,"style":1534},[100,190],"margin-right:0.0502em;",[49,1536,800],{"className":1537},[971],[49,1539],{"className":1540,"style":409},[364],[49,1542,331],{"className":1543},[413],[49,1545],{"className":1546,"style":409},[364],[49,1548,1550,1554,1557,1560,1563,1566,1569,1572,1575,1578,1581],{"className":1549},[91],[49,1551],{"className":1552,"style":1553},[95],"height:0.7667em;vertical-align:-0.0833em;",[49,1555,340],{"className":1556},[360],[49,1558],{"className":1559,"style":365},[364],[49,1561,1457],{"className":1562},[100,190],[49,1564],{"className":1565,"style":365},[364],[49,1567,340],{"className":1568},[360],[49,1570],{"className":1571,"style":365},[364],[49,1573,1462],{"className":1574,"style":1534},[100,190],[49,1576],{"className":1577,"style":897},[364],[49,1579,1481],{"className":1580},[143],[49,1582],{"className":1583,"style":897},[364],[49,1585,1587,1591,1594,1597,1600,1603,1606,1609],{"className":1586},[91],[49,1588],{"className":1589,"style":1590},[95],"height:0.6833em;",[49,1592,1484],{"className":1593},[360],[49,1595],{"className":1596,"style":365},[364],[49,1598,1457],{"className":1599},[100,190],[49,1601],{"className":1602,"style":365},[364],[49,1604,1484],{"className":1605},[360],[49,1607],{"className":1608,"style":365},[364],[49,1610,1462],{"className":1611,"style":1534},[100,190],"):\n",[49,1614,1616,1669],{"className":1615},[52],[49,1617,1619],{"className":1618},[56],[58,1620,1621],{"xmlns":60},[62,1622,1623,1666],{},[65,1624,1625,1627,1629,1631,1633,1635,1638,1642,1645,1648,1651,1653,1655,1657,1659],{},[171,1626,319],{},[75,1628,322],{},[171,1630,726],{},[75,1632,331],{},[75,1634,795],{},[71,1636,1637],{},"3.6",[171,1639,1641],{"mathvariant":1640},"normal","\u002F",[71,1643,1644],{},"6.5",[763,1646,1647],{},"  ",[75,1649,1650],{},"⟹",[763,1652,1647],{},[171,1654,726],{},[75,1656,331],{},[75,1658,795],{},[68,1660,1661,1664],{},[71,1662,1663],{},"29",[75,1665,77],{},[79,1667,1668],{"encoding":81},"\\tan \\delta = -3.6 \u002F 6.5 \\implies \\delta = -29^\\circ",[49,1670,1672,1696,1724,1742],{"className":1671,"ariaHidden":87},[86],[49,1673,1675,1678,1681,1684,1687,1690,1693],{"className":1674},[91],[49,1676],{"className":1677,"style":186},[95],[49,1679,319],{"className":1680},[360],[49,1682],{"className":1683,"style":365},[364],[49,1685,726],{"className":1686,"style":742},[100,190],[49,1688],{"className":1689,"style":409},[364],[49,1691,331],{"className":1692},[413],[49,1694],{"className":1695,"style":409},[364],[49,1697,1699,1702,1705,1709,1712,1715,1718,1721],{"className":1698},[91],[49,1700],{"className":1701,"style":910},[95],[49,1703,795],{"className":1704},[100],[49,1706,1708],{"className":1707},[100],"3.6\u002F6.5",[49,1710],{"className":1711,"style":409},[364],[49,1713],{"className":1714,"style":409},[364],[49,1716,1650],{"className":1717},[413],[49,1719],{"className":1720,"style":409},[364],[49,1722],{"className":1723,"style":409},[364],[49,1725,1727,1730,1733,1736,1739],{"className":1726},[91],[49,1728],{"className":1729,"style":186},[95],[49,1731,726],{"className":1732,"style":742},[100,190],[49,1734],{"className":1735,"style":409},[364],[49,1737,331],{"className":1738},[413],[49,1740],{"className":1741,"style":409},[364],[49,1743,1745,1749,1752,1755],{"className":1744},[91],[49,1746],{"className":1747,"style":1748},[95],"height:0.7574em;vertical-align:-0.0833em;",[49,1750,795],{"className":1751},[100],[49,1753,994],{"className":1754},[100],[49,1756,1758,1761],{"className":1757},[100],[49,1759,101],{"className":1760},[100],[49,1762,1764],{"className":1763},[112],[49,1765,1767],{"className":1766},[116],[49,1768,1770],{"className":1769},[120],[49,1771,1773],{"className":1772,"style":96},[124],[49,1774,1775,1778],{"style":127},[49,1776],{"className":1777,"style":132},[131],[49,1779,1781],{"className":1780},[136,137,138,139],[49,1782,77],{"className":1783},[143,139]," .\nAdjusting for direction: Since the grade is increasing from ",[49,1786,1788,1806],{"className":1787},[52],[49,1789,1791],{"className":1790},[56],[58,1792,1793],{"xmlns":60},[62,1794,1795,1803],{},[65,1796,1797,1799,1801],{},[71,1798,212],{},[171,1800,1641],{"mathvariant":1640},[71,1802,498],{},[79,1804,1805],{"encoding":81},"1\u002F16",[49,1807,1809],{"className":1808,"ariaHidden":87},[86],[49,1810,1812,1815],{"className":1811},[91],[49,1813],{"className":1814,"style":910},[95],[49,1816,1805],{"className":1817},[100]," to ",[49,1820,1822,1840],{"className":1821},[52],[49,1823,1825],{"className":1824},[56],[58,1826,1827],{"xmlns":60},[62,1828,1829,1837],{},[65,1830,1831,1833,1835],{},[71,1832,212],{},[171,1834,1641],{"mathvariant":1640},[71,1836,687],{},[79,1838,1839],{"encoding":81},"1\u002F11",[49,1841,1843],{"className":1842,"ariaHidden":87},[86],[49,1844,1846,1849],{"className":1845},[91],[49,1847],{"className":1848,"style":910},[95],[49,1850,1839],{"className":1851},[100],", the full dip must be beyond the second direction.\nResult: ",[20,1854,1855,1856],{},"Full Dip Direction = ",[49,1857,1859,1878],{"className":1858},[52],[49,1860,1862],{"className":1861},[56],[58,1863,1864],{"xmlns":60},[62,1865,1866,1875],{},[65,1867,1868],{},[68,1869,1870,1873],{},[71,1871,1872],{},"223",[75,1874,77],{},[79,1876,1877],{"encoding":81},"223^\\circ",[49,1879,1881],{"className":1880,"ariaHidden":87},[86],[49,1882,1884,1887,1891],{"className":1883},[91],[49,1885],{"className":1886,"style":96},[95],[49,1888,1890],{"className":1889},[100],"22",[49,1892,1894,1898],{"className":1893},[100],[49,1895,1897],{"className":1896},[100],"3",[49,1899,1901],{"className":1900},[112],[49,1902,1904],{"className":1903},[116],[49,1905,1907],{"className":1906},[120],[49,1908,1910],{"className":1909,"style":96},[124],[49,1911,1912,1915],{"style":127},[49,1913],{"className":1914,"style":132},[131],[49,1916,1918],{"className":1917},[136,137,138,139],[49,1919,77],{"className":1920},[143,139],[36,1922,1923,1926,2113,2239,2240,1401],{},[20,1924,1925],{},"Find Rate of Full Dip:",[49,1927,1929,1982],{"className":1928},[52],[49,1930,1932],{"className":1931},[56],[58,1933,1934],{"xmlns":60},[62,1935,1936,1979],{},[65,1937,1938,1940,1942,1944,1946,1948,1950,1952,1955,1957,1959,1961,1963,1969,1971,1977],{},[71,1939,212],{},[171,1941,1641],{"mathvariant":1640},[71,1943,687],{},[75,1945,331],{},[75,1947,786],{"stretchy":785},[71,1949,212],{},[171,1951,1641],{"mathvariant":1640},[171,1953,1954],{},"x",[75,1956,800],{"stretchy":785},[171,1958,340],{},[75,1960,322],{},[75,1962,786],{"stretchy":785},[68,1964,1965,1967],{},[71,1966,1872],{},[75,1968,77],{},[75,1970,795],{},[68,1972,1973,1975],{},[71,1974,595],{},[75,1976,77],{},[75,1978,800],{"stretchy":785},[79,1980,1981],{"encoding":81},"1\u002F11 = (1\u002Fx) \\cos(223^\\circ - 194^\\circ)",[49,1983,1985,2003,2072],{"className":1984,"ariaHidden":87},[86],[49,1986,1988,1991,1994,1997,2000],{"className":1987},[91],[49,1989],{"className":1990,"style":910},[95],[49,1992,1839],{"className":1993},[100],[49,1995],{"className":1996,"style":409},[364],[49,1998,331],{"className":1999},[413],[49,2001],{"className":2002,"style":409},[364],[49,2004,2006,2009,2012,2016,2019,2022,2025,2028,2031,2034,2063,2066,2069],{"className":2005},[91],[49,2007],{"className":2008,"style":910},[95],[49,2010,786],{"className":2011},[917],[49,2013,2015],{"className":2014},[100],"1\u002F",[49,2017,1954],{"className":2018},[100,190],[49,2020,800],{"className":2021},[971],[49,2023],{"className":2024,"style":365},[364],[49,2026,340],{"className":2027},[360],[49,2029,786],{"className":2030},[917],[49,2032,1890],{"className":2033},[100],[49,2035,2037,2040],{"className":2036},[100],[49,2038,1897],{"className":2039},[100],[49,2041,2043],{"className":2042},[112],[49,2044,2046],{"className":2045},[116],[49,2047,2049],{"className":2048},[120],[49,2050,2052],{"className":2051,"style":96},[124],[49,2053,2054,2057],{"style":127},[49,2055],{"className":2056,"style":132},[131],[49,2058,2060],{"className":2059},[136,137,138,139],[49,2061,77],{"className":2062},[143,139],[49,2064],{"className":2065,"style":897},[364],[49,2067,795],{"className":2068},[143],[49,2070],{"className":2071,"style":897},[364],[49,2073,2075,2078,2081,2110],{"className":2074},[91],[49,2076],{"className":2077,"style":910},[95],[49,2079,613],{"className":2080},[100],[49,2082,2084,2087],{"className":2083},[100],[49,2085,620],{"className":2086},[100],[49,2088,2090],{"className":2089},[112],[49,2091,2093],{"className":2092},[116],[49,2094,2096],{"className":2095},[120],[49,2097,2099],{"className":2098,"style":96},[124],[49,2100,2101,2104],{"style":127},[49,2102],{"className":2103,"style":132},[131],[49,2105,2107],{"className":2106},[136,137,138,139],[49,2108,77],{"className":2109},[143,139],[49,2111,800],{"className":2112},[971],[49,2114,2116,2149],{"className":2115},[52],[49,2117,2119],{"className":2118},[56],[58,2120,2121],{"xmlns":60},[62,2122,2123,2146],{},[65,2124,2125,2127,2129,2131,2133,2135,2141,2143],{},[171,2126,1954],{},[75,2128,331],{},[71,2130,687],{},[171,2132,340],{},[75,2134,322],{},[68,2136,2137,2139],{},[71,2138,1663],{},[75,2140,77],{},[75,2142,331],{},[71,2144,2145],{},"9.6",[79,2147,2148],{"encoding":81},"x = 11 \\cos 29^\\circ = 9.6",[49,2150,2152,2171,2230],{"className":2151,"ariaHidden":87},[86],[49,2153,2155,2159,2162,2165,2168],{"className":2154},[91],[49,2156],{"className":2157,"style":2158},[95],"height:0.4306em;",[49,2160,1954],{"className":2161},[100,190],[49,2163],{"className":2164,"style":409},[364],[49,2166,331],{"className":2167},[413],[49,2169],{"className":2170,"style":409},[364],[49,2172,2174,2177,2180,2183,2186,2189,2192,2221,2224,2227],{"className":2173},[91],[49,2175],{"className":2176,"style":96},[95],[49,2178,687],{"className":2179},[100],[49,2181],{"className":2182,"style":365},[364],[49,2184,340],{"className":2185},[360],[49,2187],{"className":2188,"style":365},[364],[49,2190,994],{"className":2191},[100],[49,2193,2195,2198],{"className":2194},[100],[49,2196,101],{"className":2197},[100],[49,2199,2201],{"className":2200},[112],[49,2202,2204],{"className":2203},[116],[49,2205,2207],{"className":2206},[120],[49,2208,2210],{"className":2209,"style":96},[124],[49,2211,2212,2215],{"style":127},[49,2213],{"className":2214,"style":132},[131],[49,2216,2218],{"className":2217},[136,137,138,139],[49,2219,77],{"className":2220},[143,139],[49,2222],{"className":2223,"style":409},[364],[49,2225,331],{"className":2226},[413],[49,2228],{"className":2229,"style":409},[364],[49,2231,2233,2236],{"className":2232},[91],[49,2234],{"className":2235,"style":479},[95],[49,2237,2145],{"className":2238},[100]," .\nResult: ",[20,2241,2242,2243,483,2271],{},"Rate of Full Dip = ",[49,2244,2246,2259],{"className":2245},[52],[49,2247,2249],{"className":2248},[56],[58,2250,2251],{"xmlns":60},[62,2252,2253,2257],{},[65,2254,2255],{},[71,2256,212],{},[79,2258,212],{"encoding":81},[49,2260,2262],{"className":2261,"ariaHidden":87},[86],[49,2263,2265,2268],{"className":2264},[91],[49,2266],{"className":2267,"style":479},[95],[49,2269,212],{"className":2270},[100],[49,2272,2274,2287],{"className":2273},[52],[49,2275,2277],{"className":2276},[56],[58,2278,2279],{"xmlns":60},[62,2280,2281,2285],{},[65,2282,2283],{},[71,2284,2145],{},[79,2286,2145],{"encoding":81},[49,2288,2290],{"className":2289,"ariaHidden":87},[86],[49,2291,2293,2296],{"className":2292},[91],[49,2294],{"className":2295,"style":479},[95],[49,2297,2145],{"className":2298},[100],[11,2300,2302],{"id":2301},"field-workflow","Field Workflow",[2304,2305,2306,2311,2314,2318,2321,2325,2328,2332],"steps",{},[2307,2308,2310],"h3",{"id":2309},"observe-apparent-dips","Observe Apparent Dips",[16,2312,2313],{},"Identify two lines on the plane where the gradient (apparent dip) and the compass bearing can be measured .",[2307,2315,2317],{"id":2316},"sketch-the-problem","Sketch the Problem",[16,2319,2320],{},"Plot the two bearings. Note that the full dip direction must lie \"between\" the two observed directions if they are on either side of the peak, or \"beyond\" them if the grade is strictly increasing .",[2307,2322,2324],{"id":2323},"calculate-direction","Calculate Direction",[16,2326,2327],{},"Use the tangent formula to find the bearing of the strike line or full dip .",[2307,2329,2331],{"id":2330},"calculate-rate","Calculate Rate",[16,2333,2334,2335,2374],{},"Apply the ",[49,2336,2338,2356],{"className":2337},[52],[49,2339,2341],{"className":2340},[56],[58,2342,2343],{"xmlns":60},[62,2344,2345,2353],{},[65,2346,2347,2349,2351],{},[171,2348,340],{},[75,2350,322],{},[171,2352,287],{},[79,2354,2355],{"encoding":81},"\\cos \\phi",[49,2357,2359],{"className":2358,"ariaHidden":87},[86],[49,2360,2362,2365,2368,2371],{"className":2361},[91],[49,2363],{"className":2364,"style":300},[95],[49,2366,340],{"className":2367},[360],[49,2369],{"className":2370,"style":365},[364],[49,2372,287],{"className":2373},[100,190]," correction to find the maximum gradient .",[11,2376,2378],{"id":2377},"practical-tips","Practical Tips",[33,2380,2381,2580],{},[36,2382,2383,2386,2387,2451,2452,23,2516,1401],{},[20,2384,2385],{},"Strike Line Check:"," If you find the direction of full dip is ",[49,2388,2390,2409],{"className":2389},[52],[49,2391,2393],{"className":2392},[56],[58,2394,2395],{"xmlns":60},[62,2396,2397,2406],{},[65,2398,2399],{},[68,2400,2401,2404],{},[71,2402,2403],{},"180",[75,2405,77],{},[79,2407,2408],{"encoding":81},"180^\\circ",[49,2410,2412],{"className":2411,"ariaHidden":87},[86],[49,2413,2415,2418,2422],{"className":2414},[91],[49,2416],{"className":2417,"style":96},[95],[49,2419,2421],{"className":2420},[100],"18",[49,2423,2425,2428],{"className":2424},[100],[49,2426,108],{"className":2427},[100],[49,2429,2431],{"className":2430},[112],[49,2432,2434],{"className":2433},[116],[49,2435,2437],{"className":2436},[120],[49,2438,2440],{"className":2439,"style":96},[124],[49,2441,2442,2445],{"style":127},[49,2443],{"className":2444,"style":132},[131],[49,2446,2448],{"className":2447},[136,137,138,139],[49,2449,77],{"className":2450},[143,139],", then the strike lines (where the level is constant) must run exactly ",[49,2453,2455,2474],{"className":2454},[52],[49,2456,2458],{"className":2457},[56],[58,2459,2460],{"xmlns":60},[62,2461,2462,2471],{},[65,2463,2464],{},[68,2465,2466,2469],{},[71,2467,2468],{},"090",[75,2470,77],{},[79,2472,2473],{"encoding":81},"090^\\circ",[49,2475,2477],{"className":2476,"ariaHidden":87},[86],[49,2478,2480,2483,2487],{"className":2479},[91],[49,2481],{"className":2482,"style":96},[95],[49,2484,2486],{"className":2485},[100],"09",[49,2488,2490,2493],{"className":2489},[100],[49,2491,108],{"className":2492},[100],[49,2494,2496],{"className":2495},[112],[49,2497,2499],{"className":2498},[116],[49,2500,2502],{"className":2501},[120],[49,2503,2505],{"className":2504,"style":96},[124],[49,2506,2507,2510],{"style":127},[49,2508],{"className":2509,"style":132},[131],[49,2511,2513],{"className":2512},[136,137,138,139],[49,2514,77],{"className":2515},[143,139],[49,2517,2519,2538],{"className":2518},[52],[49,2520,2522],{"className":2521},[56],[58,2523,2524],{"xmlns":60},[62,2525,2526,2535],{},[65,2527,2528],{},[68,2529,2530,2533],{},[71,2531,2532],{},"270",[75,2534,77],{},[79,2536,2537],{"encoding":81},"270^\\circ",[49,2539,2541],{"className":2540,"ariaHidden":87},[86],[49,2542,2544,2547,2551],{"className":2543},[91],[49,2545],{"className":2546,"style":96},[95],[49,2548,2550],{"className":2549},[100],"27",[49,2552,2554,2557],{"className":2553},[100],[49,2555,108],{"className":2556},[100],[49,2558,2560],{"className":2559},[112],[49,2561,2563],{"className":2562},[116],[49,2564,2566],{"className":2565},[120],[49,2567,2569],{"className":2568,"style":96},[124],[49,2570,2571,2574],{"style":127},[49,2572],{"className":2573,"style":132},[131],[49,2575,2577],{"className":2576},[136,137,138,139],[49,2578,77],{"className":2579},[143,139],[36,2581,2582,2585,2586,2642],{},[20,2583,2584],{},"Reciprocal Ratios:"," In these formulas, it is often easier to work with gradients as decimals (",[49,2587,2589,2612],{"className":2588},[52],[49,2590,2592],{"className":2591},[56],[58,2593,2594],{"xmlns":60},[62,2595,2596,2609],{},[65,2597,2598,2600,2602,2604,2606],{},[71,2599,212],{},[171,2601,1641],{"mathvariant":1640},[71,2603,498],{},[75,2605,331],{},[71,2607,2608],{},"0.0625",[79,2610,2611],{"encoding":81},"1\u002F16 = 0.0625",[49,2613,2615,2633],{"className":2614,"ariaHidden":87},[86],[49,2616,2618,2621,2624,2627,2630],{"className":2617},[91],[49,2619],{"className":2620,"style":910},[95],[49,2622,1805],{"className":2623},[100],[49,2625],{"className":2626,"style":409},[364],[49,2628,331],{"className":2629},[413],[49,2631],{"className":2632,"style":409},[364],[49,2634,2636,2639],{"className":2635},[91],[49,2637],{"className":2638,"style":479},[95],[49,2640,2608],{"className":2641},[100],") to avoid confusion .",[11,2644,2646],{"id":2645},"common-mistakes","Common Mistakes",[33,2648,2649,2655],{},[36,2650,2651,2654],{},[20,2652,2653],{},"Sign Errors:"," Forgetting that the full dip must be the steepest possible line. If your calculated full dip is flatter than your observed apparent dip, your math is wrong .",[36,2656,2657,2660,2661,2689,2690,2694],{},[20,2658,2659],{},"Angular Difference:"," The angle ",[49,2662,2664,2677],{"className":2663},[52],[49,2665,2667],{"className":2666},[56],[58,2668,2669],{"xmlns":60},[62,2670,2671,2675],{},[65,2672,2673],{},[171,2674,287],{},[79,2676,290],{"encoding":81},[49,2678,2680],{"className":2679,"ariaHidden":87},[86],[49,2681,2683,2686],{"className":2682},[91],[49,2684],{"className":2685,"style":300},[95],[49,2687,287],{"className":2688},[100,190]," is the ",[2691,2692,2693],"em",{},"difference"," between the full dip direction and the apparent dip direction, not the bearing itself .",[11,2696,2698],{"id":2697},"faq","FAQ",[2700,2701,2702,2709,2715],"accordion",{},[2703,2704,2706],"accordion-item",{"label":2705},"What is a 'Strike Line' used for?",[16,2707,2708],{},"In site grading, a strike line is used to set out \"contours\" on a plane. Any two points on a strike line have the exact same elevation .",[2703,2710,2712],{"label":2711},"Can I find full dip with only one measurement?",[16,2713,2714],{},"No. You need at least two apparent dip measurements in different directions to uniquely define the 3D plane .",[2703,2716,2718],{"label":2717},"How is this used in volumes?",[16,2719,2720],{},"By knowing the dip and strike of a rock stratum, you can calculate the \"wedge\" of rock that needs to be excavated before you even start digging .",[11,2722,2724],{"id":2723},"conclusion","Conclusion",[16,2726,2727,2728,2785],{},"Dip and strike calculations allow the surveyor to model complex 3D surfaces from just a few field observations. By mastering the ",[49,2729,2731,2755],{"className":2730},[52],[49,2732,2734],{"className":2733},[56],[58,2735,2736],{"xmlns":60},[62,2737,2738,2752],{},[65,2739,2740,2742,2744,2746,2748,2750],{},[171,2741,319],{},[75,2743,322],{},[171,2745,173],{},[171,2747,340],{},[75,2749,322],{},[171,2751,287],{},[79,2753,2754],{"encoding":81},"\\tan \\theta \\cos \\phi",[49,2756,2758],{"className":2757,"ariaHidden":87},[86],[49,2759,2761,2764,2767,2770,2773,2776,2779,2782],{"className":2760},[91],[49,2762],{"className":2763,"style":300},[95],[49,2765,319],{"className":2766},[360],[49,2768],{"className":2769,"style":365},[364],[49,2771,173],{"className":2772,"style":191},[100,190],[49,2774],{"className":2775,"style":365},[364],[49,2777,340],{"className":2778},[360],[49,2780],{"className":2781,"style":365},[364],[49,2783,287],{"className":2784},[100,190]," formula, you can provide engineers with critical data on subsurface rock layers and optimize the design of site slopes.",[11,2787,2789],{"id":2788},"references","References",[16,2791,2792,2793,2796],{},"Schofield, W. (2001). ",[2691,2794,2795],{},"Engineering Surveying",". 5th ed. Butterworth-Heinemann.",{"title":2798,"searchDepth":2799,"depth":2799,"links":2800},"",2,[2801,2802,2803,2804,2805,2812,2813,2814,2815,2816],{"id":13,"depth":2799,"text":14},{"id":30,"depth":2799,"text":31},{"id":153,"depth":2799,"text":154},{"id":446,"depth":2799,"text":447},{"id":2301,"depth":2799,"text":2302,"children":2806},[2807,2809,2810,2811],{"id":2309,"depth":2808,"text":2310},3,{"id":2316,"depth":2808,"text":2317},{"id":2323,"depth":2808,"text":2324},{"id":2330,"depth":2808,"text":2331},{"id":2377,"depth":2799,"text":2378},{"id":2645,"depth":2799,"text":2646},{"id":2697,"depth":2799,"text":2698},{"id":2723,"depth":2799,"text":2724},{"id":2788,"depth":2799,"text":2789},"Earthworks","A technical guide to calculating the direction and rate of full dip from apparent dip observations on tilted stratum planes.","md","\u002Fimages\u002Fdip-strike.jpg",{"authorCredentials":2822,"commentCount":2823,"tags":2824,"relatedTools":2829,"relatedArticles":2832,"sources":2835},"P.Eng",0,[2825,2817,2826,2827,2828],"Dip and Strike","Geology","Math","Site Grading",[2830,2831],"Scientific Calculator","Geological Compass",[2833,2834],"mass-haul-diagrams-earthwork-economics","prismoidal-vs-end-area-volumes",[2836],{"title":2837,"type":2838,"note":2839},"Engineering Surveying (Fifth Edition)","Book","Primary source for the mathematical relationship between full and apparent dip.",true,"\u002Fblog\u002Fdip-and-strike-geological-surveying","2024-04-13",12,{"title":5,"description":2818},{"loc":2841},"blog\u002F26.dip-and-strike-geological-surveying","aeqVAcmdiQ6JrInRB2dXlN8ViW9yXz5SeCOL8e_cu2c",[2849,2854],{"title":2850,"path":2851,"stem":2852,"description":2853,"children":-1},"Machine Guidance: Integrating RTK GPS with Construction Plant","\u002Fblog\u002Fmachine-guidance-rtk-gps-construction","blog\u002F25.machine-guidance-rtk-gps-construction","A technical look at how RTK GPS and digital ground models are used to automate earthmoving machinery, eliminating the need for traditional setting-out stakes.",{"title":2855,"path":2856,"stem":2857,"description":2858,"children":-1},"Laser Safety: Hazard Classes and Management on the Construction Site","\u002Fblog\u002Flaser-safety-and-management-on-site","blog\u002F27.laser-safety-and-management-on-site","A comprehensive guide to the safety requirements, hazard classifications, and professional responsibilities when using lasers for setting out and alignment.",1783851944473]