Question

10.) kelly is flying a kite to which the angle of elevation is 70°. the string on the kite is 65 meters long. how far is the kite above the ground?

Explanation:

Step1: Set up trig - relation

We have a right - triangle where the length of the string is the hypotenuse ($c = 65$ m) and the height of the kite above the ground is the side opposite the angle of elevation ($\theta=70^{\circ}$). We use the sine function $\sin\theta=\frac{opposite}{hypotenuse}$. Let $h$ be the height of the kite above the ground. So, $\sin\theta=\sin(70^{\circ})=\frac{h}{65}$.

Step2: Solve for $h$

We can rewrite the equation as $h = 65\times\sin(70^{\circ})$. Since $\sin(70^{\circ})\approx0.9397$, then $h = 65\times0.9397 = 61.0805\approx61.1$ m.

Answer:

$61.1$ m