Question

As observed from the top of a $75m$ high lighthouse from the sea-level, the angles of depression of two ships arc ${30}^o$ and ${45}^o$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

• A. $75\sqrt{3}-1m$
• B. $40\sqrt{4}-1m$
• C. $69\sqrt{6}-1m$
• D. $72\sqrt{3}-1m$

Answer 1

The correct option is A $75\sqrt{3}-1m$

$\tan {30}^0=\frac{75}{BC}.......1$

$\tan {45}^0=\frac{75}{BC-x}.........2$

From $1$ & $2$

$BC-x=BC\times \frac{1}{\sqrt{3}}(BC=75+x)$

$75=(75+x)\frac{1}{\sqrt{3}}$

$75(\sqrt{3}-1)=x$ Ans.