Question

How do you solve and how many solutions does the triangle have if you are given angle A = 69.8 degrees, side a = 74.5, side b = 21.3?

Answer 1

Solve triangle knowing A = 69.8; a = 74.5, and b = 21.3

Explanation:

Find angle b, given a = 74.5, b = 21.3, and sin A = sin 69.8 = 0.94

sin B = (b.sin A)/a = 21.3(0.94)/74.5 = 0.268 ->
There are 2 solutions for angle B
B = 15.59
or B = 180 - 15.59 = 164,41. Rejected because b = 21.3 < a = 74.5

Angle C = 180 - A - B = 180 - 69.8 - 15.59 = 94.61

Side `c = (a.sin C)/(sin A) = 74.5(0.99/0.94)` = 78,46