Question

KiteKite StringAltitude : 120 ftGroundA kite is flown at a 55° angle of elevation. That is, the kite stringmakes a 55° angle with the ground.If the altitude of the kite is 120 feet, what is the length of the kitestring used? Round your answer to the nearest foot.

Answer 1

Given:

The altitude of the kite, h=120 ft.

The angle made by the kite string with the ground, θ=55° .

Let x be the length of the string.

Now, using trigonometric property in the above triangle,

$\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{hypotenuse} \\ \sin \theta=\frac{h}{x} \end{gathered}$

Now, substitute the values and solve the equation for x.

$\begin{gathered} \sin 55^{\circ}=\frac{120\text{ ft}}{x} \\ x=\frac{120\text{ ft}}{\sin55^{\circ}} \\ =146.49\text{ ft} \\ \approx146\text{ ft} \end{gathered}$

Therefore, length of the kite string is 146 ft.