Question

In triangle ABC, AB = 90 in., BC = 80 in., and angle B measures 50°. What is the approximate perimeter of the triangle?

Answer 1

A. 242.4 in

Explanation:

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Answer 2

The answer to your question is Perimeter = 287.3 in

Explanation:

AB = 90 in

BC = 80 in

∠B = 50

Perimeter = ?

Process

1.- We need to find AC using Law of sines

`(sin A)/(80) = (sin 50)/(90)`

`sin A = (80)/(90) sin 50`

`sin A = 0.68`

A = 42.9 ≈ 43

The sum of the internal angles in a triangle equals 180°

A + B + C = 180°

43 + B + 50 = 180

B = 180 - 43 - 50

B = 87°

`(AC)/(Sin 87) = (90)/(sin 50)`

`AC = 90 (sin 87)/(sin 50)`

AC = 117.3

2.- Find the perimeter

Perimeter = AB + BC + AC

Perimeter = 90 + 80 + 117.3

Perimeter = 287.3 in