Question

quinn is flying a kite. the angle of elevation formed by the kite string and the ground is 40°, and the kite string forms a straight segment that is 100 feet long. explain how to find the distance between the ground and the kite. include a description of the triangle you drew to help you solve, including the variables and measurements you assigned to each side and angle. round your answer to the nearest foot.

Explanation:

Step1: Draw a right - triangle

Draw a right - triangle where the length of the kite string is the hypotenuse ($c = 100$ feet), the angle of elevation $\theta=40^{\circ}$, and the height of the kite above the ground is the side opposite the angle of elevation, let's call it $a$. The ground distance from the person flying the kite to the point directly below the kite is the adjacent side.

Step2: Use the sine function

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin\theta=\sin(40^{\circ})=\frac{a}{c}$. Since $c = 100$ feet, we can solve for $a$: $a = c\times\sin\theta$.

Step3: Calculate the value of $a$

Substitute $c = 100$ and $\theta = 40^{\circ}$ into the formula. $\sin(40^{\circ})\approx0.6428$, so $a=100\times0.6428 = 64.28\approx64$ feet.

Answer:

64 feet