Question

How do you solve and how many solutions does the triangle have if you are given angle C = 115 degrees, side b = 54.8, side c = 53.4?

Answer 1

Use the trig identity: sin A/a = sin B/b

Explanation:

`sin A = (b.sin C)/c = (54.8(0.90))/53.4 = 49.32/53.4 = 0.92`

sin A = 0.92 -> A = 66.92 deg, and A = 180 - 66.92 = 111.08
The result A = 111.08 is rejected because C = 115.
Angle B = 180 - A - C = 180 - 66.92 - 115 =`-1.92`
Angle B could not be negative, then the given data doesn't match.
Side lengths b and c are not correct.