Question

The top of a broken tree has it's top touching the ground (shown in the adjoining figure) at a distance of $10m$ from the bottom. If the angle made by the broken part with the ground is ${30}^o$, then the length of the broken part is:

• A. $10\sqrt{3}m$
• B. $\frac{20}{\sqrt{3}}m$
• C. $20m$
• D. $20\sqrt{3}m$

Answer 1

Answer: (B)

$\frac{20}{\sqrt{3}}m$

The tree broke at point B, and touches the ground at A. The roots are at point C.
Now, the distance between the top of broken part and the roots $=10m$
Considering it as a triangle system,$△ABC$ is a right angled triangle.
$\cos {30}^o=\frac{Perpendicular}{Hypotenuse}=\frac{AC}{AB}$
$\frac{\sqrt{3}}{2}=\frac{10}{AB}$
$\therefore$ Length of broken part $AB=\frac{20}{\sqrt{3}}m$