Question

In ΔABC, a = 4 inches, b = 5.8 inches and ∠C=99°. Find ∠B, to the nearest 10th of an degree.

Answer 1

m∠B = 49.4°

Explanation:

Use the law of cosines to get side c, and then the law of sines to get angle B

`c^(2) = a^(2) + b^(2) - 2ab cos C\\ = 4^(2) + 5.8^(2) - 2(4)(5.8) cos 99\\ = 16 + 33.64 + 7.25855\\ = 56.25855\\c = √(56.25855) = 7.543`

sin C/c = sin B/b

sin 99/7.543 = sin B/5.8

sin B = 5.8 sin 99/7.543

= .75945

m∠B = arcsin .75945 = 49.4°