Question

A kite is flying at a height of $45$ 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 ${60}^0$. Find the length of the string assuming that there is no slack in the string.

Answer 1

Let $C$ be the position of kite above the ground such that it subtends an angle of ${60}^o$ at point $A$ on the ground.

Let the length of the string be $AC=l$ m.

Given, $BC=45$ m and $\angle BAC={60}^o$.

In $\Delta ABC,$

$\sin {60}^{\circ }=\frac{BC}{AC}$

$\Rightarrow \frac{\sqrt{3}}{2}=\frac{45}{l}$

$\Rightarrow l=\frac{45\times 2}{\sqrt{3}}=\frac{90}{\sqrt{3}}$

$=30\sqrt{3}$

So, the length of the string is $30\sqrt{3}$ m.