Question

triangle ABC is right angled at A and triangle PQR is right angled at P . if cos B = cos Q , show angle B = angle Q

Answer 1

Cos B = AB/BC

Cos Q = PQ/PR

Given AB/BC = PQ/PR. So AB/PQ = BC/ PR

In triangles ABC and PQR

Angle A = Angle P = 90

AB/PQ = BC/ PR

So Δ ABC ≈ Δ PQR (Sas similarity criterion)

∠B = ∠Q