Question

In right angled ∆LMN, if ∠N = θ, ∠M = 90°, cos θ = 24/25, find sin θ and tan θ. Similarly, find (sin² θ) and (cos² θ).

Answer 1

i. cos θ = 24/25

In ∆LMN, ∠M = 90°, ∠N = θ

Let the common multiple be k. 

∴ MN = 24k and LN = 25k 

Now, LN² = LM² + MN² … [Pythagoras theorem] 

∴ (25k)² = LM² + (24k)² 

∴ 625 k² = LM² + 576k² 

∴ LM² = 625k² – 576k²

∴ LM² = 49k² 

∴ LM = √49k² ...[Taking square root of both sides] 

= 7k