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?
Answer & explanation
Correct answer: option 4
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