Q) As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 60°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3 = 1.73)

Ans:

Let’s consider AB is the tower and 2 ship are at C & D.

In Δ ABC,

tan 60⁰ =   

√3 = 

AC = 25 √3

In Δ ABD,

tan 30⁰ =  

d + 25√3 = 75 √3

d = 50 √3 = 50 x 1.73 = 86.5

Therefore, the distance between the two ships is 86.5 m