Question

As observed from the top of a 150 m high lighthouse from the sea level, the angles of depression of the two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

पर्याय

• `150 (sqrt3 + 1)`

• `150 (sqrt3 - 1)`

• `150/((sqrt3 - 1))`

• `150/((sqrt3 + 1))`

Answer 1

`150 (sqrt3 - 1)`

Explanation:

Here Lighthouse BC = 150 m

In Δ BDC,

BD = BC = 150m (using tan 45°)

In Δ ABC,

`"AB = BC" sqrt3` (using tan 30°)

`"AB" = 150sqrt3`

Hence distance AD = `150 (sqrt3 - 1)`