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 8 m. Find the height of the tree?

• A. 15√3m
• B. 20√3m
• C. 11√3m
• D. 8√3m

Answer 1

The correct option is D

8√3m

Let AC (= H) be the original height of the tree and BC = h

Let BC be the distance between foot of tree and top of tree, A’C = 8 m

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

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

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

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

$\Rightarrow$ A’B =($\frac{16}{\sqrt{3}}$) m

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