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) 



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 



