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 of ${30}^{\circ }$ with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

Answer 1

Let AC was the original tree. Due to storm, it was broken into two parts. The broken part A'B is making 30° with the ground.

In triangle A'BC,
$\tan 30=\frac{BC}{A^{\prime }C}$
$\frac{1}{\sqrt{3}}=\frac{BC}{8}$

$BC=\frac{8}{\sqrt{3}}$

Also,
$\cos 30=\frac{A^{\prime }C}{A^{\prime }B}$

$\frac{8}{A^{\prime }B}=\frac{\sqrt{3}}{2}$
$A^{\prime }B=\frac{16}{\sqrt{3}}$

height of the tree = A'B + BC = $\frac{16}{\sqrt{3}}+\frac{8}{\sqrt{3}}=8\sqrt{3}$m