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