Question

A pole stands vertically inside a triangular park $ABC$. Let the angle of elevation of the top of the pole from each corner of the park be $\frac{\pi }{3}$. If the radius of the circumcircle of $\Delta ABC$ is $2$, then the height of the pole is equal to:

• A. $\frac{1}{\sqrt{3}}$
• B. $\sqrt{3}$
• C. $2\sqrt{3}$
• D. $\frac{2\sqrt{3}}{3}$

Answer 1

The correct option is C $2\sqrt{3}$


Let the height of the pole be $h$, then
$\tan {60}^{\text{o}}=\frac{h}{2}\Rightarrow h=2\sqrt{3}$