Question

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is ${60}^{\circ }$. Find the length of the string, assuming that there is no slack in the string.

• A. $20\sqrt{3}$ m
• B. $30$ m
• C. $30\sqrt{3}$ m
• D. $60$ m

Answer 1

The correct option is A

$20\sqrt{3}$ m

The situation can be represented by the figure below:

In the given right-angled triangle:
$sin\left(\angle ACB\right)=\frac{AB}{AC}$
$\Rightarrow sin{60}^{\circ }=\frac{AB}{AC}$
$\Rightarrow AC=\frac{AB}{sin{60}^{\circ }}=\frac{30}{\frac{\sqrt{3}}{2}}=\frac{60}{\sqrt{3}}=20\sqrt{3}$
$\therefore$ Length of the string is $20\sqrt{3}m.$