Question

An aeroplane at an altitude of 1500 metres, finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships

Answer 1

A is the aeroplane, D and C are the ships sailing towards A. Ships are sailing towards the aeroplane in the same direction.

In the figure, height AB=1500 m

To find: Distance between the ships, that is CD.

Solution:

In the right-angled ΔABC

`tan 45^@ = (AB)/(BC)`

`=> 1 = 1500/(BC)`

=> BC = 1500 m

In the right-angled ΔABD,

`tan 30^@ = (AB)/(BD)`

`=> 1/sqrt3 = 1500/(BD)`

`=> BD = 1500sqrt3`

=> BD = 1500(1.732)  = 2598 m

∴ Distance between the ships = CD = BD - BC

= 2598 - 1500

= 1098 m