Question

A circus artist is climbing a 20 m long rope Which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is ${30}^{\circ }$

• A. $10m$
• B. $9m$
• C. $12m$
• D. $8m$

Answer 1

The correct option is A $10m$

Based on the given information, we can draw the figure shown above.

Let the height of the pole be $hm$.
and $AC=20m$ be the rope which the circus artist is climbing.

Given, $\angle ACB={30}^{\circ }$

We know that, $\sin \theta =\frac{\text{Opposite Side}}{\text{Hypotenuse}}$

Hence, in $\Delta ABC$,

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

$=\frac{h}{20}$
$\Rightarrow \frac{h}{20}=\frac{1}{2}[\because \sin {30}^o=\frac{1}{2}]$

$\Rightarrow h=\frac{1}{2}\times 20$

$=10m$

Hence, the height of the pole is $10m$.