Question

From the top of a light house, an abserver looking at a boat makes an angle of depression of 600. If the height of the lighthouse is 90 m then find how far is the boat from the lighthouse. (3 = 1.73)

Answer 1

Let AB be the light house.
The boat is at C and observer is at A.
∠ MAC is the angle of depression.
∠ MAC = ∠ ACB = 60° .....(Alternate angle)
AB = 90 m.
From the figure, tan60° `= (AB)/(BC)`
`sqrt3 = (90)/(BC)`
`BC = (90)/(sqrt3) = (90 xx sqrt3)/(sqrt3 xxsqrt3) = (90sqrt3)/3 = 30sqrt3`
∴ BC = 30 × 1.73
∴ BC = 51.90
∴ The boat is at a distance of 51.90m from the light house.