A man standing at the top of a tower finds that a boat coming towards the tower takes 10 minutes for the angle of depression to change from 30° to 60°. How much more time will be taken by the boat to reach the tower?

5 minutes

CD = 10 min and BD = ?

In Δ ABC

tan30° = AB/BC

⇒ 1/√3 = AB/BC

⇒ AB = BC/√3     --- (1)

In ΔABD

tan 60° = AB/BD

⇒ √3 = AB/BD

⇒ AB = √3 BD     --- (2)

From equation (1) equation (2)

BC/√3 = √3 BD

⇒ BC = 3 BD

As we know,

BC = BD + CD

⇒ 3BD = BD + 10

⇒ 2BD = 10

⇒ BD = 10/2

⇒ BD = 5 min