Question

Solve the triangle.

B = 72°, b = 12, c = 8


A. Cannot be solved
B. C = 39.3°, A = 68.7°, a ≈ 16.5
C. C = 39.3°, A = 68.7°, a ≈ 11.8
D. C = 44.5°, A = 63.7°, a ≈ 11.8

Answer 1

Solving the triangle.
B=72 , b =12, c = 8
Using the sine rule
b/sin B= c/sin C
thus; 12/sin 72 = 8/sin C
sin C = 8/12.618
C= 39.3

The sum of angles in a triangle add up to 180°
Therefore, A +B+C=180
A = 180- (72+39.25)
= 68.7

Using the sine rule
a/sin A= b/sin b
therefore; a/sin 68.7 = 12/sin 72
a = (sin 68.7) ×12/sin 72
= (sin 68.7) ×12.618
= 11.756
≈ 11.8