Question

Two poles of equal height are standing opposite to each other on either side of a road which is 100 m wide. Find a point between them on road, angles of elevation of their tops are ${30}^{\circ }$ and ${60}^{\circ }$. The height of each pole in meter, is:

• A. $25\sqrt{3}$
• B. $20\sqrt{3}$
• C. $28\sqrt{3}$
• D. $30\sqrt{3}$

Answer 1

The correct option is A $25\sqrt{3}$

In $△AOC$,

$\tan {60}^o=\frac{h}{x}$ $\therefore x=\frac{h}{\sqrt{3}}$

In $△BOD$,

$\tan {30}^o=\frac{h}{100-x}$

$\frac{1}{\sqrt{3}}=\frac{h}{100-x}$ $100-x=h\sqrt{3}$

$100-h\sqrt{3}=x$ $x=\frac{h}{\sqrt{3}}$

$\therefore 100-h\sqrt{3}=\frac{h}{\sqrt{3}}$

$\therefore h=25\sqrt{3}m$

$\therefore x=\frac{h}{\sqrt{3}}=\frac{25\sqrt{3}}{\sqrt{3}}$

$\therefore x=25m$

$\therefore OC=25m$ and $OD=75m$.