Question

In right angled ∆PQR, ∠Q = 90°, ∠R = θ and if sin θ = 5/13, then find cos θ and tan θ.

Answer 1

i. Take the given trigonometric ratio as 13k equation (i). 

sin θ = 5/13 .. .(i) [Given] 

By using the definition write the trigonometric ratio of sin θ and take it as equation (ii). 

In right angled ∆PQR, ∠R = θ

Let the common multiple be k. 

∴ PQ = 5k and PR = 13k 

Find QR by using Pythagoras theorem.

PR² = PQ² + QR² … [Pythagoras theorem] 

∴ (13k)² = (5k)² + QR² 

∴ 169k² = 25k² + QR² 

∴ QR² = 169k² – 25k² 

= 144k² 

∴ QR = √(144k²) . . . [Taking square root of both sides] 

= 12k