Question

As observed from the top of a $75$ 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

In $△ABC$,

$\frac{AB}{BC}=\tan {45}^o,BC=75$m

In $△ABD$,

$\frac{AB}{BD}=\tan {30}^o$

$\Rightarrow \frac{75}{BC+CD}=\frac{1}{\sqrt{3}}$

$\Rightarrow \frac{75}{75+CD}=\frac{1}{\sqrt{3}}$

$\therefore CD=\left[75\right(\sqrt{3}-1\left)\right]$m