Question

A straight highway leads to the foot of a tower. A man standing at the top
of the tower observes a car at an angle of depression of 30°, which is
approaching the foot of the tower with a uniform speed. After covering a
distance of 50 m, the angle of depression of the car becomes 60°. Find the
height of the tower. ​

Answer 1

The height of the tower is 25√3 m.

• Using the first angle of depression,

                tan30° = height of tower / distance of car

                1/√3  = height of tower / distance of car                              

                Distance of car = √3  height of tower                ………..1

• After coverings 50 meters,

               tan60° = height of tower / (distance of car – 50)

               √3 =  height of tower / (distance of car – 50)      ………..2

               Putting value from 1 in 2,

              √3 =  height of tower / ( √3  height of tower – 50)

              Height of tower = 25√3 m