Question

A kite is flying at a height of 45 m above the ground. The string attached to the kite is temporarily tide 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.

Answer 1

Let C be the position of kite above the ground such that it subtends an angle of ${60}^{\circ }$ at point A on the ground.
Suppose the length of the string, $AC$ be $lm$.
Given, BC =45 m and $\angle BAC={60}^{\circ }$.
IN $\Delta ABC:$
$\sin {60}^{\circ }=\frac{BC}{AC}\because \sin \theta =\left[\frac{Perpendicular}{Hypotensue}\right]$
therefore, $\frac{\sqrt{3}}{2}=\frac{45}{l}$
$\Rightarrow l=\frac{45\times 2}{\sqrt{3}}=\frac{90}{\sqrt{3}}=30\sqrt{3}$
Thus, the length of the string is $30\sqrt{3}m$.