Question

From the top of the lighthouse, an observer looks at a ship and finds the angle of depression to be 30°. If the height of the lighthouse is 100 metres, then find how far the ship is from the lighthouse.

Answer 1

Let AB represent the height of lighthouse and point C represent the position of the ship.

Angle of depression ∠PAC 30° 

AB = 100m. 

Now, ray AP || seg BC 

∴ ∠ACB = ∠PAC … [Alternate angles] 

∴ ∠ACB = 30° AB = 100m 

In right angled ∆ABC, 

tan 30° = AB/BC  …[By definition] 

∴ 1/√3 = 100/BC

∴ BC = 100√3 m 

∴ The ship is 100√3 m far from the lighthouse.