Question

An observer flying in an aeroplane at an altitude of 900m observes 2 ships in front of him, which are in the same direction at an angles of depression of
60 and 30 respectively. find the distance between the two ships

Answer 1

one at angle of depression 60 degree will be at distance of 900/$\sqrt{3}$ 
second at angle of depression of 30 degree will be at a distance 900$\sqrt{3}$

Answer 2

See the attachment.
We need to find the distance between the ships which is CD (=y-x).

In ΔABC,
tan 60 = AB/BC
⇒ √3 = 900/x
⇒ x = 900/√3 = 300√3m

In ΔABD,
tan 30 = AB/BD
⇒ 1/√3 = 900/y
⇒ y = 900×√3 = 900√3m

CD = y-x = 900√3 - 300√3 = 600√3 m 

So the distance between the two ships is 600√3 m.