a case in Spherical Trigonometry. 



313 



N. P. D. 



AR 



As a matter of course, the very same method can be applied 

 to the converse case ; that in which the two angles and the in- 

 terjacent side are known, and the third angle required. 



Let A and B be the known angles, y the interjacent side, 

 then a similar method would give 



4 cos C =^ } —2 cos(A — B) + cos (A — B — y) + cos (A — B + ^) ) 

 \ ._ 2 cos (A -j- B) — cos (A + B — y) — cos (A + B + 9.) f * 



or, if we put A — B = D, A + B = S 



4co3C = i""^''°^^"^''°^^^ — y) + c''«(^ + 5')) 

 ) — 2 cos S — cos (S — y) — cos (S + y) I ' 



I subjoin a single example. 



Two angles of a triangle, being 37° IT and 4*1° 22 ; and 

 their interjacent side 57° 29' ; required the third angle : 



