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

Solution:

It is given that

∠C is a right angle = 90°

sin A = sin B

Here

∠a = ∠b …. (1)

We know that ∠a + ∠b = 90°

As ∠a + ∠b + ∠c = 180° we get ∠c = 90°

So ∠a + ∠a = 90° …. (2)

From equation (1) and (2)

2∠a = 90° 

Dividing both sides by 2

∠a = 45°

Therefore, m ∠a is 45°.

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

Summary:

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