Q47 / 90 · JEE Main 2021 (18 Mar Shift 2) · Mathematics

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

Solution

Let $P D = h, R = 2$

As angle of elevation of top of pole from $A, B, C$ are equal So $D$ must be circumcentre of $Δ A B C$

$\tan (\frac{π}{3}) = \frac{P D}{R} = \frac{h}{R}$

$h = R \tan (\frac{π}{3}) = 2 \sqrt{3}$

Hence, the correct answer is option: 'B'.