Question

Two persons are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter person is
A. a/4
B. a/√2
C. a√2
D.a/2√2

Answer 1

Two persons are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary.

The height of the shorter person is a/2√2.

Option D is correct.

Consider the attached figure while going through the following steps.

In Δ APB,

tan ∅  = AB / BP

= h / (a/2)

⇒ tan ∅  = 2h/a .........(1)

In Δ CDP,

cot (90 - ∅) = PD / CD

tan ∅ = (a/2) / 2h

⇒ tan ∅ = a/4h .........(2)

comparing (1) and (2), we get,

2h/a = a/4h

8h^2 = a^2

h^2 = a^2 / 8

h = a / 2√2