Question

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

Answer 1

Answer:

m∠B = 49.4°

Step-by-step explanation:

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

$c^{2} = a^{2} + b^{2} - 2ab cos C\\ = 4^{2} + 5.8^{2} - 2(4)(5.8) cos 99\\ = 16 + 33.64 + 7.25855\\ = 56.25855\\c = \sqrt{56.25855} = 7.543$

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°