Question

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle ${30}^{\circ }$ with it. 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?

• A. $15\sqrt{3}m$
• B. $20\sqrt{3}m$
• C. $11\sqrt{3}m$
• D. $8\sqrt{3}m$

Answer 1

The correct option is D

$8\sqrt{3}m$

Let AC(H) be the original height of the tree

Let BC = h

Let BC be the distance between foot of tree and top of tree, A’C = 20m

Given angle of elevation BA’C = ${30}^{\circ }$

In ΔA’BC, Tan ${30}^{\circ }$ = $\frac{BC}{A^{\prime }C}$

$h=\left(\frac{8}{\sqrt{3}}\right)m$

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

$\Rightarrow A^{\prime }B=\left(\frac{16}{\sqrt{3}}\right)m$

Height of Tree
= BC + A’B
= h + A’B
$=\left(\frac{8}{\sqrt{3}}\right)+\left(\frac{16}{\sqrt{3}}\right)=\left(\frac{24}{\sqrt{3}}\right)=8\left(\sqrt{3}\right)m$