Question

Solve the triangle. A = 46°, a = 31, b = 27

A. B = 38.8°, C = 115.2°, c ≈ 34.3

B. B = 38.8°, C = 95.2°, c ≈ 25.7

C. B = 38.8°, C = 95.2°, c ≈ 42.9

D. Cannot be solved

Answer 1

C. B=38.8, C=95.2, c=42.9

Explanation:

Find B by using sine rule

sin 46/31=sin B/27

sin B= 27 sin 46/31

B=sin‐¹(0.627)

B=38.8

Find C

C= 180-(A+B)

C=180-(38.8+46)

C=95.2

Using sine rule, Find c

31/sin 46=c/sin 95.2

c=31 sin 95.2/sin 46

c=42.9