Question

Two men standing on same side of a pillar $75$ meter high, observe the angles of elevation of the top pillar to be ${30}^{\circ }$ and ${60}^{\circ }$ respectively the distance between two men is:

• A. $50\surd 3m$
• B. $100m$
• C. $\frac{75}{\sqrt{3}}m$
• D. None of these

Answer 1

The correct option is A $50\surd 3m$

Let $AB$ denotes the pillar

Let $C$ & $D$ be two women respectively

To find $CD$ i.e distance between two men

$\frac{BA}{AD}=\tan {30}^o$

$\frac{75}{AD}=\frac{1}{\sqrt{3}}$

$AD=75\sqrt{3}m$

$\frac{BA}{AC}=\tan {60}^o$

$\frac{75}{AC}=\sqrt{3}$

$\frac{75}{\sqrt{3}}m=AC$

$\therefore CD=AD-AC=75\sqrt{3}-\frac{75}{\sqrt{3}}$

$CD=\frac{225-75}{\sqrt{3}}=\frac{150}{\sqrt{3}}=50\sqrt{3}m$

$\therefore$ Distance between two women $=50\sqrt{3}m$