Question

In triangle ABC, ∠A and ∠B are complementary, where cos A = 0.24. What is the measure, to the nearest degree of, ∠B?

Answer 1

`m\angle B=14^o`

Explanation:

we know that

In this problem, if angle A and angle B are complementary, then triangle ABC is a right triangle

If two angles are complementary, then their sum is equal to 90 degrees and the cofunction identities state that the sine of one equals the cosine of the other and vice versa

so

sin(A)=cos(B)

cos(A)=sin(B)

we have

`cos(A)=0.24`

therefore

`sin(B)=cos(A)=0.24`

Find the measure of angle B

`m\angle B=sin^(-1)(0.24)=14^o`