Question

A kite flying 40 feet in the air (perpendicular to the ground) is attached to a string held on the ground by a stake. The string makes angle of 60° with the ground. How long is the string. Round to the nearest hundredth.

Answer 1

Given:

AB is the height from the ground to the kite.

AC is the length of the string.

$\begin{gathered} \sin 60=\frac{AB}{AC} \\ \frac{\sqrt[]{3}}{2}=\frac{40}{AC} \\ AC=\frac{40\times2}{\sqrt[]{3}} \\ AC=\frac{80}{\sqrt[]{3}} \\ AC=\frac{80\sqrt[]{3}}{3} \\ AC=46.19\text{ feet} \end{gathered}$

Length of the string is 46.19 feet