Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle ${60}^o$ with it. The distance between the foot of the tree to the point where the top touches the ground is $3m$. Find the height of the tree.

Answer 1

$\tan {60}^{\circ }=\frac{OA}{OB}\sqrt{3}=\frac{OA}{3}\Rightarrow OA=\sqrt{3}\sin {60}^{\circ }=\frac{OA}{AB}\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{AB}\Rightarrow AB=2$

Height of tree $=OA+AB=\sqrt{3}+2$