Question

As observed from the top of a $75m$ high lighthouse from the sea-level, the angles of depression of two ships are ${30}^o$ and ${60}^o$. If one strip is exactly behind the other on the same side of the light-house then the distance between the two ships is:

• A. $25\sqrt{3}m$
• B. $75\sqrt{3}m$
• C. $50\sqrt{3}m$
• D. None of these

Answer 1

The correct option is C $50\sqrt{3}m$

Consider the given figure
$\tan {60}^0$
$=\sqrt{3}$
$=\frac{75}{y}$
Hence
$y=25\sqrt{3}$
$\tan {30}^0$
$=\frac{75}{x+y}$
$=\frac{1}{\sqrt{3}}$
Hence
$x+y=75\sqrt{3}$
$x=75\sqrt{3}-y$
$=75\sqrt{3}-25\sqrt{3}$
$=50\sqrt{3}m$
$=AB$
= Distance between the ships.