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 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Answer 1

Let AC be the broken part of the tree.
$\therefore$Total height of the tree $=AB+AC$
In right $\Delta ABC$,
cos ${30}^{\circ }=\frac{BC}{AC}$
$\Rightarrow \frac{\sqrt{3}}{2}=\frac{8}{AC}$
$\Rightarrow AC=\frac{16}{\sqrt{3}}$
Also, $tan{30}^{\circ }=\frac{AB}{BC}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{8}$
$\Rightarrow AB=\frac{8}{\sqrt{3}}$
Therefore, the total height of the tree $=AB+AC=\frac{8}{\sqrt{3}}+\frac{16}{\sqrt{3}}=\frac{24}{\sqrt{3}}$ = $8\sqrt{3}$ m.