Question

Robin is flying a kite. She ties the 50 foot kite string to the ground. If the kite is40 feet high, what is the measure of the angle the string forms with the ground?

Answer 1

Let us start with the sketch of the figure

Using the trigonometric functions to obtain the measure of the angle.

From the image above,

`\begin{gathered} \text{Hypotenuse}=50ft \\ \text{Opposite}=40ft \\ \theta=\text{?} \end{gathered}`

Thus, the trigonometric function that correlates both the opposite and the hypotenuse together is the Sine of angles.

`\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}`

Solving for θ

`\begin{gathered} \sin \theta=(40)/(50)=(4)/(5)=0.8 \\ \sin \theta=0.8 \\ \therefore\theta=\sin ^(-1)0.8=53.1301\approx53.13^0(nearest\text{ 2 decimal places)} \\ \therefore\theta=53.13^0 \end{gathered}`

Hence, the measure of the angle the string forms with the ground is

`53.13^0`