Question

A person is climbing a long rope stretched from the top of the pole and fixed at the ground. The height of the pole is $20$ m and the angle made by the rope with the ground is ${30}^o$. The length of the rope is

• A. $30$ m
• B. $10$ m
• C. $40$ m
• D. $\frac{40}{\sqrt{3}}$ m

Answer 1

The correct option is C $40$ m

Let the length of the rope is $AC$

Then, $\sin {30}^{\circ }=\frac{AB}{AC}$

$\Rightarrow \frac{1}{2}=\frac{20}{AC}$

$\Rightarrow AC=2\times 20$

$\Rightarrow AC=40m$