Question

Billy is flying a kite. The kite string makes an angle of67° with the ground. If Billyis standing 100 feet from thepoint on the ground directly below the kite, find the length ofthe kite string. Round the measure of the kite string to the nearest hundredth.

Answer 1

The given situation is represented in the right triangle above, x is the length of the kite string.

To find x (hypotenuse) use the next trigonometric ratio for angle 67º:

$cos67º=\frac{100ft}{x}$

Solve x:

$\begin{gathered} x*cos67º=100ft \\ x=\frac{100ft}{cos67º} \\ \\ x\approx255.93ft \end{gathered}$Then, the length of the kite string is 255.93 feet