Archive image from page 274 of Deep borehole surveys and problems. Deep borehole surveys and problems deepboreholesurv00hadd Year: 1931 PROBLEMS 263 Let A be an outcrop and D a point in the workings with C the base of the borehole -BO in the same or projected plane. We have given the angles a of the borehole dip and 7 the surface slope so that the apex angles a and j8 shown are deduced. We desire the length xoryoi the known length DA x -\- y. X _ DC _ DC-CB ~ CA Fig. 176. sin a' sin BAC y CB • CA sin BDC sin /3 sin a sin (f + /3) sin (f — a) sin /3 Expanding we get a form comparable with
Archive image from page 274 of Deep borehole surveys and problems. Deep borehole surveys and problems deepboreholesurv00hadd Year: 1931 PROBLEMS 263 Let A be an outcrop and D a point in the workings with C the base of the borehole -BO in the same or projected plane. We have given the angles a of the borehole dip and 7 the surface slope so that the apex angles a and j8 shown are deduced. We desire the length xoryoi the known length DA x -\- y. X _ DC _ DC-CB ~ CA Fig. 176. sin a' sin BAC y CB • CA sin BDC sin /3 sin a sin (f + /3) sin (f — a) sin /3 Expanding we get a form comparable with Eq. (27) above X _ cot j8 + cot f y cot Expanding and collecting cot f (x + ) Again sm a - cot f X cot a — y cot jS sin (f + /3) (46) sin (f - a') sin jS sin (f - D) sin A sin Z) sin (r + A) X cot jD - - cot f Expanding as before y cot A + cot f Cross multiplying and collecting as before cot f (x + y) = y cot D — x cot A (47) From Eqs. (46) and (47) note that X cot a' — 7/ cot fi =y cot D — X cot A Now solve for x or y since a',,D,A, and a; + ?/ are known. r/ie Length of the Borehole.—Having obtained either x or y (and applying the lateral deviation angle if the points
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