Question

Solve the triangle.

a =23.5 b= 15.6 c=14.4
What is the degree measure of angle A?
What is the degree measure of angle B?
What is the degree measure of angle C?

Answer 1

The measure of

angle A = 76.9

angle B = 50.3°

angle C = 62.8°

We use cosine and sine rule to get the measure of A , B and C

sine rule states mathematically that;

a² = c² + b² + 2bc cosA

23.5² = 15.6² + 14.4²+ 2 × 15.6 × 14.4cos A

552.25 = 450.72 + 449.28cosA

552.25 - 450.72 = 449.28cosA

cosA = 101.53/449.28

cosA = 0.226

A = 76.9°

Using sine rule

a/sin A = b/sinB

23.5/sin 76.9 = 15.6/sinB

23.5 sinB = 15.19

sinB = 15.19/23.5

sinB = 0.646

B = 40.3°

C = 180 - ( 40.3 + 76.9)

C = 180 - 117.2

C = 62.8°