Question

Solve the triangle.

B = 73°, b = 15, c = 8
Select one:
a. C = 35.9°, A = 71.3°, a ≈ 15.2
b. C = 30.7°, A = 76.3°, a ≈ 15.2
c. C = 30.7°, A = 76.3°, a ≈ 21.3
d. Cannot be solved

Answer 1

Using the sine law of triangles to solve for angle C:

b / sin B = c / sin C

C = arcsin (c * sin B / b)
C = 30.7°

Since interior angles of a triangle always add up to 180°, we can use this to solve for angle A:

angle A = 180° - 73° - 30.7°
angle A = 76.3°

Having solved for angle A, we can solve for side a using the sine law.

a / sin A = b / sin B

a = b * sin A / sin B
a = 15.2

Therefore, the correct answer is B.