Question

A kite is flying at a height of $60$ 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 $60$. Find the length of the string, assuming that there is no slack in the string.

• A. $40\sqrt{3}$ m
• B. $30\sqrt{3}$ m
• C. $20\sqrt{3}$ m
• D. $10\sqrt{3}$ m

Answer 1

The correct option is A $40\sqrt{3}$ m

Given, the height of the kite $AB$ is $60$ m and it makes an angle of elevation at point $C$ of ${60}^0$.

In right angled $△ABC$, we have

$cosec{60}^0=\frac{AC}{AB}$

$\Rightarrow \frac{2}{\sqrt{3}}=\frac{AC}{60}$

$\Rightarrow AC=60\times \frac{2}{\sqrt{3}}$

$\Rightarrow AC=60\times \frac{2\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$

$\Rightarrow AC=40\sqrt{3}$ m