Question

An aeroplane at an altitude of 1200 m finds that two ships are sailing towards it in the same direction. The angles of depression of the ships as observed from the aeroplane are 30o and 60o respectively. Find the distance between the two ships

Answer 1

Answer:

Let the aeroplane be at B and let the two ships be at C and D such that their angles of depression from B are 60∘  and 30∘ respectively.

We have AB = 1200 metres. Let AC = x and CD = y.

In ΔCAB , we have. 

tan60∘=CAAB

⇒3=x1200

⇒x=31200=4003

In ΔBAD , we have 

tan30∘=ADAB

⇒31=x+y1200

⇒x+y=12003

⇒y=12003−x

⇒y=12003−4003=8003=800