A pole stands vertically inside a triangular park ABC . Let the...

Let $PD = h, R = 2$

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

$\tan \left(\dfrac{\pi}{3}\right) = \dfrac{PD}{R} = \dfrac{h}{R}$

$h = Rtan\left(\dfrac{\pi}{3}\right) = 2\sqrt{3}$