Question

An aeroplane when 3000 m high passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are $60\degree$ and $45\degree$ respectively. The vertical distance between the two aeroplanes is

• A. 1268 m
• B. 1500m
• C. 3000m
• D. 1200m

Answer 1

Answer: (A)

1268 m

Answer 2

In $\triangle$ABC
tan 60°=$\frac{3000}{BC}$
BC = $\frac{3000}{\sqrt{3}}$m ………..(i)
In $\triangle$BCD
tan 45°=$\frac{3000 - h}{BC}$
BC = 3000 − h ……. (ii)
Equating and solving equations (i) and (ii), we get
h = 1268m
So the correct option is (A).