Question

In right triangle ABC, angle C is a right angle and sin A = sin B. What is the measure of angle A?

A. 30
B. 45
C. 60
D. 75

Answer 1

Answer: (B)45

Explanation:

Answer 2

Given that ABC is a right triangle.

∠C is a right angle. ∠C = 90° and sin A = sin B

We need to determine the measure of angle A.

Measure of ∠A:

Let the angles of A and B be x.

By triangle sum property, we get;

`\angle A+\angle B+\angle C=180^(\circ)`

Substituting the values, we get;

`x+x+90=180`

Adding the terms, we get;

`2x+90=180`

Simplifying the terms, we have;

`2x=90`

`x=45`

Hence, the measure of ∠A = 45° and the measure of ∠B = 45°

Thus, Option B is the correct answer.