Question

From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 84 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)

Answer 1

As shown in the figure, assume AB as the lighthouse and let A be the position of the observer and C be the position of the ship. Let the distance from the ship to the lighthouse be x.

Let AB be the height of the lighthouse,

∴ AB = 84 metres [Given]

The point 'C' be the position of the ship,

∴ ∠ ACB = 60°

`tan 60° = ("Opposite side of "60°) /("Adjacent side of "60°)`

∴ `tan 60° = "AB" / "BC"`

∴ `sqrt3 = 84/"BC"`

∴ `"BC" = 84/sqrt3`

∴ `"BC" = (84/sqrt3)×sqrt3/sqrt3`

∴ BC =  28√3

∴ BC = 28× 1.73

∴ BC = 48.4 m.

∴ The ship is 48.4 m away from the lighthouse.