Question

There are two possible triangles with the measures given for triangle ABC.

b = 20.2, c = 18.3, C = 38°

What are the possible measures of angle B? Round your answer to the nearest whole number.
A.4°
B.4° and 176°
C.43°
D.43° and 137°

Answer 1

D

Explanation:

Answer 2

First, apply the Law of Sines:


`(sinC)/(c)= (sinB)/(b)`

And solve for B:


`sinB= (bsinC)/(c)`


`B= sin^(-1)( (bsinC)/(c) )`

B = sin⁻¹(20.2 × sin38 / 18.3)
= sin⁻¹(0.67958)

There are two angles that are a possible solution: 43° and 137° and both can be angles of a triangle (B + C < 180°).

Therefore, the correct answer is D) 43° and 137°.