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)

Question

Responses

.625°.625 degrees

38.68°38.68 degrees

77.36°77.36 degrees

90°90 degrees

Answer 1

To find the angle of elevation of the kite, we can use the sine function from trigonometry. The height of the kite (opposite side) is 50 meters, and the length of the string (hypotenuse) is 80 meters.

The sine of the angle of elevation \( \theta \) is given by:

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

Calculating this gives:

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

Now, we can find \( \theta \) by taking the arcsine (inverse sine) of 0.625:

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

Calculating this using a calculator:

\[ \theta \approx 38.68° \]

Thus, the angle of elevation of the kite is approximately 38.68 degrees.

So the correct response is:

38.68°