Question

In triangle ABC, AB= √3a, AC = a and BC = 2a. Prove that ∟A = 90˚

Answer 1

The sides AB , BC and AC are Pythagoras triplets.
i.e.

BC² = AC² +AB²
BC² = (2a)² = 4a²
and, AC² + AB² = (a)² + (√3a)³ = a² + 3a² = 4a²

So, Angle opposite to side BC is Right angle.
i.e. ∠A = 90°