Question

brian is flying a kite over a field at the end of a 65 m string. if the angle of elevation to the kite measures 70°, how high above the ground is the kite?

Explanation:

Step1: Set up the trigonometric relationship

We can consider 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 opposite side ($a$) with respect to the angle of elevation ($\theta=70^{\circ}$). Using the sine function: $\sin\theta=\frac{a}{c}$.

Step2: Solve for the height $a$

Substitute $\theta = 70^{\circ}$ and $c = 65$ m into the formula $a = c\times\sin\theta$. So, $a=65\times\sin(70^{\circ})$.
We know that $\sin(70^{\circ})\approx0.9397$. Then $a = 65\times0.9397=61.0805\approx61.1$ m.

Answer:

The kite is approximately $61.1$ m above the ground.