sin 78° 14' 30", co ar... 0.0092103 sin 40° 5′ 30′′, log....... 9.8088942 Now to find the third side c, we have the tion, sin B: sin C:: sin b: sin c. propor Example III. Suppose we have given the angle A=112° 25', the angle B=73° 15′, and the contained side c=24° 38′ to find the rest. hence we shall obtain the values of the sides a and b by computing, as follows: The number corresponding to this logarithm in the tables, is 76° 29′ 18′′; but since cos negative, therefore (equ. 1.) tan A+B is 2 a+b is also nega tive; hence we must take the supplement of the angle in the tables for the value of a+b We have 2 To find the angle C, we have, sin b sin c :: sin B: sin C. sin 99° 19′ 16′′ 5....... 9.9942272 sin C............ 9.6068817 ... C=23° 51′ 27′′ · 5. Example IV. Let there be given the side a=75°33′, the side b-18° 5′, and the angle A=130° to find the angles B and C and the third side. To find the angle B, we have, Now, there are two angles answering to this logarithmic sine, viz: 14° 12′ 51′′, and its supplement ; but the latter being greater than A, is inadmissible; we must therefore restrict our choice to the former. Hence, B=14° 12′ 51′′. 46° 49' A+B =28° 44' =72° 6′ 25′′ 1 |