Question

Given right Triangle ABC, Angle B = 60, C = 45 and perimeter = 12cm, find the length of all three sides?

Answer 1

A = 180 - B - C = 180 - 60 - 45 = 75

`a/sin A = b/sin B = c/sinC = 12/(sin A + sin B + sin C) = 12/2.55 = 4.71`
sin A = sin 75 = 0.97
sin B = sin 60 = 0.87
sin C = sin 45 = 0.71
sin A + sin B + sin C = 2.55

a = 4.71.sin A = 4.71.(0.97) = 4.57
b = 4.71 sin B = 4.71.(0.87) = 4.10
c = 4.71.(sin C) = 4.71.(0.71) = 3.33

Check; a + b + c = 12 OK