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°

Option B is correct.

Step-by-step 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

       (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.