Question

In right triangle ABC, ∠C is a right angle, and sin A = sin B. What is m∠A?

A. 30°
B. 45°
C. 60°
D. 75°

Answer 1

In right triangle ABC, if ∠C is a right angle and sin A = sin B, then ∠A and ∠B are congruent, and m∠A is 45°.

Step-by-step explanation:

In right triangle ABC, if ∠C is a right angle and sin A = sin B, then ∠A and ∠B are congruent. Since the sum of the angles in a triangle is 180°, the remaining angle (∠C) must be 90°.

Since ∠A and ∠B are congruent, let's assume their value to be 'x'.

Now, we know that the sum of all angles in a triangle is 180°. Therefore, we can write the equation as follows:

x + x + 90° = 180°.

Simplifying the equation, we get: 2x + 90° = 180°. Subtracting 90° from both sides, we have 2x = 90°. Dividing both sides by 2, we find x = 45°.

Hence, m∠A is 45°.