Question

From the top of a lighthouse, an observer looking at a ship makes angle of

depression of 60°. If the height of the lighthouse is 90 metre, then find how far

the ship is from the lighthouse. ( 3 =1.73)​

Answer 1

Let AB be the height of the lighthouse,

∴ AB = 90 metres [Given]

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

∴ ∠ ACB = 600

tan 600 = Opposite side of 600 / Adjacent side of 600

∴ tan 600 = AB / BC

∴ √3 = 90/BC

∴ BC = 90/√ 3

∴ BC = (90/√3)× √3/√3

∴ BC = 30√3

∴ BC = 30× 1.73

∴ BC = 51.9 m.

∴ The ship is 51.9 m away from the lighthouse.