Question

A helicopter is at an altitude of 200 metres. Finds that two boats are sailing towards it in the same direction. The angle of depression of the boats as observed from helicopter are 45° & 60° respectively. Find the distance between two boats?

Answer 1

Distance between the two boats is `color(brown)(84.53` `color(brown)(m`

Explanation:

Two boats are at C & B and helicopter is at A, 200 m above point B on the ground.

Given : `AB = 200 m, hat(PAC) = hat( ACB) = 45^@, hat(PAD) = hat (ADB) = 60^@`

To find the distance between the two boats `bar(CD)`

`tan hat(ACB) = tan 45 = 200 / (CB)`

`bar(CB) = 200 / tan 45 = 200 / 1 = 200 m`

Similarly, #bar(DB) = 200 / tan 60 = 200 / sqrt3 = 115.47 m#

`bar(CD) = bar (CB) - bar(DB) = 200 - 115.47 = color (brown)(84.53 m`

Distance between the two boats is `color(brown)(84.53` `color(brown)(m`