Question

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to the ground. The inclination of the string with the ground is 60^o . Find the length of the string, assuming that there is no slack in the string.

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{m}\mathrm{be}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{string}. \\ \mathrm{Given}:\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{kite},\mathrm{PQ}=60\mathrm{m}\mathrm{and}\mathrm{angle}\mathrm{of}\mathrm{elevation},\mathrm{\theta }=60° \\ \mathrm{Now},\sin \mathrm{\theta }=\frac{\mathrm{perpendicular}}{\mathrm{hypotenuse}}=\frac{PQ}{PR} \\ \Rightarrow \sin 60°=\frac{60}{x} \\ \Rightarrow \frac{\sqrt{3}}{2}=\frac{60}{x} \\ \Rightarrow x=\frac{120}{\sqrt{3}}=\frac{120}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}} \\ \Rightarrow x=\frac{120\sqrt{3}}{3}=40\sqrt{3} \\ \Rightarrow x=40\times 1.73=69.2 \\ \therefore \mathrm{The}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{string}\mathrm{is}69.2\mathrm{m}. \end{gathered}$$