Q) A straight highway leads to the foot of a tower. A man standing on the top of the 75 m high tower observes two cars at angles of depression of 30° and 60°, which are approaching the foot of the tower. If one car is exactly behind the other on the same side of the tower, find the distance between the two cars. (Use √3 = 1.73)

Ans:

Let’s consider AB be the tower and 2 cars are at points 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 cars is 86.5 m