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

45 degrees has two equal angles

Answer 2

Option B is correct.

Explanation:

Given ∠C is a right angle in Δ ABC

sin A = sin B

To find: m∠A

Figure is attached.

Consider,

sin A = sin B

`(CB)/(AB)=(CA)/(AB)` (using trigonometric ratio)

⇒ CB = CA

Δ ABC is isosceles right angled triangle,

using result, angles opposite to equal sides are equal in ΔABC.

we get,

∠A = ∠B

Now using angle sum property of triangle,

∠A + ∠B + ∠C = 180°

2∠A + 90 = 180

2∠A = 90

∠A = 45°

Therefore, Option B is correct.