Question

The poles of two lamps are of equal height A boy standing exactly at the mid of the poles finds its angle of elevation 45°. While moving 15 m towards one pole, he finds the angle of elevation of the top of that pole 60°. The height of the pole and the distance between them is approximately :

(A) 15 and 30 m

(B) 23.1 and 46.2 m

(C) 35.5 and 71 m

(D) 23.1 and 35.55 m

Answer 1

Answer is (C) 35.5 and 71 m

Let two poles are AB and PQ of height h m.

Distance between in these boles BQ = 2x. 

Point C is between these points which is mid-point of BQ.

From ΔPQC, tan 45°= PQ/CQ

⇒ l = h/x

⇒ h = x …..(i)

The angle of elevation of top of pole from point D is 60°.

This  point D is 15 m distance from point C in the side of pole. So that

DQ = CQ – CD = (x – 15)m

From right angled ΔPQD

∴ Distance between points 

= 2x = 2h

= 2 × 35.5 = 71 m