Question

A straight tree breaks due to storm and the broken part bends so that the top of tree touches the ground making an angle of ${30}^o$ with the ground. The distance from the foot of the tree to the point where the top touches the ground is $10$ meters. The height of the tree is :

• A. $10(\sqrt{3}+1)m$
• B. $10\sqrt{3}m$
• C. $10(\sqrt{3}-1)m$
• D. $\frac{10}{\sqrt{3}}m$

Answer 1

The correct option is B $10\sqrt{3}m$

Let $AC$ be the broken part of tree and $CB$ be the remaining part of tree.

In $\Delta ABC$

${\tan 30}^0=\frac{BC}{10}$

$\Rightarrow BC=\frac{10}{\sqrt{3}}m$

Again

${\cos 30}^0=\frac{AB}{AC}$

$\Rightarrow \frac{\sqrt{3}}{2}=\frac{10}{AC}$

$\Rightarrow AC=\frac{20}{\sqrt{3}}$

height of the tree will be $=AC+BC=\frac{20}{\sqrt{3}}+\frac{10}{\sqrt{3}}=\frac{30}{\sqrt{3}}=10\sqrt{3}m$

Correct answer : Option B.