PARTICULARLY APPLICABLE TO SOME GEODETICAL PROBLEMS. 131 



A A 



Putting a:b = (l>, .rc = v/,, we have 



^ + <lr = A, !HL^_ sin/3.sin {y -C) 

 sin x/, sin 7 . sin (ji -B)' 



Again, to find cp and f we may use any one of the eight formulae 

 of Art. 27 and 28, the eighth for instance, viz., 



find e so that tan 6 = ?^ sin (0 + >/,), 

 fa.. J sin . , 



^^" ^ 9-8794988 



si" (7 - C) 9-6814280 



'"^^'"7 OO6OI677 



1 ^ sin (fi-B) 0-0046088 



sin A=: 99" . 5' . 49"'2) 9-9945029 



tan (0= 22 . 38 . 21 9) 96202062 



s"'' ^ 9-5853822 



1-Hsin (0 + ^ = 121 . 44 . 11 1)0-0703374 



s^" ^ 9-9945029 



A 



tan (^ = a;b= 24 . 4 .49-6)9-6502225 



^ = xc = {A-(f>)= 75 . .59-6) 



The angles xl, xc being now known, all the angles of the triangles 

 about the point D may be found by addition atid subtraction. 



To verify the .solution we may try whether the angles cp and ,/. 



satisfy the condition $i^ = *^" ^ This will rpnnir. . 



sui >// sin (0 + >//) ■ require no more lo- 



garithms than will be wanted to determine y and ss. 



Eg 



