ΔABC is a right - angle triangle at B. If tan A = \({{5} \over 12}\), then sin A + sin B + sin C will be equal to:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 4)

Answer 1

Given:

tan A = \({{5} \over 12}\)

Calculation:

F1 SSC Ishita 24.02.23 D4

As we know tan = P/B and sin θ = P/H

So, H = √(P² + B²)

⇒ H = √(52 + 122)

⇒ H = √(25 + 144)

⇒ H = √169

⇒ H = 13

Now,

sin A + sin B + sin C

= sin A + sin 90° + sin C

= \({{5} \over 13}\) + 1 + \({{12} \over 13}\)

⇒ \({{5\,+\,13\,+12} \over 13}\)

⇒ \({{30} \over 13}\)

⇒ \(2{{4} \over 13}\)

∴ The required answer is \(2{{4} \over 13}\).