As observed from the top of a 150 m tall light house, the angles of depression of two ships approaching it are 30° and 45°. If one ship is directly behind the other, find the distance between the two ships.

Question

As observed from the top of a 150 m tall light house, the angles of depression of two ships approaching it are 30&#xB0; and 45&#xB0;. If one ship is directly behind the other, find the distance between the two ships.

Philoid · Accepted Answer

In ∆ABD

tan 45° =

1 =

x = 150m ………………..(1)

In ∆ABC

tan 30° =

=

x + y = 150√3 ………………..(2)

On substituting value of x from eqn (1) in eqn (2), we get

150 + y = 150√3

y = 150 (√3 - 1) ⇒ 109.8m

Therefore the distance between two ships is 109.8m