Question

A kite is flying at a height of 50 meters above the ground. The string attached to the kite is 80 meters long. Assuming the string is straight and forms an angle with the ground, what is the angle of elevation of the kite?(1 point)
Responses

.625°
.625 degrees

77.36°
77.36 degrees

90°
90 degrees

38.68°

Answer 1

To find the angle of elevation of the kite, we can use the right triangle formed by the height of the kite, the length of the string, and the distance from the point on the ground directly below the kite to the person holding the string.

The height of the kite (opposite side) is 50 meters, and the length of the string (hypotenuse) is 80 meters. We can use the sine function to find the angle of elevation \(\theta\):

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{50}{80}
\]

Calculating this gives:

\[
\sin(\theta) = \frac{50}{80} = 0.625
\]

Next, we need to find the angle \(\theta\):

\[
\theta = \arcsin(0.625)
\]

Using a calculator, we find:

\[
\theta \approx 38.68^\circ
\]

Thus, the angle of elevation of the kite is approximately **38.68°**.

So the correct response is:

**38.68°**