Question

In the triangle below, if B = 77°, 6 = 9, a = 6, use the Law of Sines to find mZC. Round your answer to the nearest tenth.

Answer 1

The sine rule is expressed as

a/SinA = b/SinB = c/SinC

where a, b and c are the length of the sides opposite angles A, B and C. From the information given,

b = 9, angle B = 77

a = 6, angle A = ?

Thus, we have

6/SinA = 9/Sin77

by crossmultiplying, we have

9SinA = 6Sin77

SinA = 6Sin77/9

SinA = 0.65

Taking the sine inverse of 0.65, we have

angle A = Sin^-1(0.65)

angle A = 40.5

Recall, the sum of the angles in a triangle is 180 degrees. This means that

A + B + C = 180

40.5 + 77 + C = 180

117.5 + C = 180

C = 180 - 117.5

angle C = 62.5 degrees