Question

From the top of a 200 m high pillar, the top and foot of another pillar respectively of 30° and 60°, make an angle of elevation. The height of the second pillar and the distance between the two pillars is in m :

(A) 400/3, 100

(B) 200/3, 100/√3

(C) 400/3, 200/√3

(D) None of these

Answer 1

Answer is (C) 400/3, 200/√3

Let a pillar of height 200 m. 

The second pillar AB is x m distance from its of height h. 

An angle of A and B from top 300 and 60°.

Hence,

∠XPA = ∠PAM = 30°

∠XPB = ∠PBQ = 60°

Let BQ = AM = x

AB = MQ = h

So, PM = PQ – MQ = (200 – h)m

From right angled ∆PQB,

tan 60° = PQ/BQ

⇒ √3 = 200/x

⇒ x = 200/√3 m

From right angled ∆PMA,