Question

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

Answer 1

Here Lighthouse BC = 150 m

In $\Delta$BDC,

BD = BC = 150m ( using tan ${45}^{\circ }$ )

In $\Delta$ABC,

AB = BC$\sqrt{3}$ ( using tan ${30}^{\circ }$ )

AB = 150$\sqrt{3}$

Hence distance AD = 150($\sqrt{3}$-1)m