Question

The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.

Answer 1

Let PQ be the light house.

`=>` PQ = 60

`tan 60^@ = (PQ)/(AQ)`

`=> sqrt(3) = 60/(AQ)`

`=> AQ = 60/sqrt(3)`

`=> AQ = (20 xx 3)/sqrt(3)`

`=> AQ = (20 xx sqrt(3) xx sqrt(3))/sqrt(3)`

`=> AQ = 20sqrt(3)  m`

In ΔPQB

`tan 45^@ = (PQ)/(QB)`

`=> 1 = 60/(QB)`

`=>` QB = 60 m

Now,

AB = AQ + QB

= `20sqrt(3) + 60`

= 20 × 1.732 + 60

= 94.64 

= 95 m