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 ${30}^o$ with the horizontal. The distance from the foot of the tree to the point where the top touches the ground is $10$ m. The height of the tree is

• A. $10(\sqrt{3}+1)$ m
• B. $10\sqrt{3}$ m
• C. $10(\sqrt{3}-1)$ m
• D. $\frac{30}{\sqrt{3}}$ m

Answer 1

The correct option is D $\frac{30}{\sqrt{3}}$ m

The broken part touches the ground, making a triangle with the ground and foot of the tree as shown in the figure.

Now,
$\tan 30=\frac{b}{10}$
$b=10\tan 30$
$b=10\times \frac{1}{\sqrt{3}}$
$\cos 30=\frac{10}{l}$
$\frac{\sqrt{3}}{2}=\frac{10}{l}$
$l=\frac{20}{\sqrt{3}}$
Therefore, length of the tree is $l+b=\frac{10+20}{\sqrt{3}}=\frac{30}{\sqrt{3}}$