Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of a 50 m high building, finds the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak.

### Answer

In ∆APQ

PQ/AP = sin 30° = 1/2

PQ = 200/2 = 100 m

PR = 100 – 50 = 50 m

In ∆PRD,

PR/PD = sin 45° = 1/√2

PD = (PR)(√2)

= 50√2 m