Question

A kite is flying at a height of 50 meters. The string of the kite makes an angle with the ground. If the length of the string is 70 meters, what angle does the string make with the ground?(1 point)
Responses

25.57°
25.57 degrees

35.57°
35.57 degrees

15.57°
15.57 degrees

45.57°

Answer 1

To find the angle that the string of the kite makes with the ground, we can use the sine function in trigonometry. The sine of an angle in a right triangle is given by the ratio of the length of the opposite side to the hypotenuse.

In this case:
- The height of the kite (opposite side) = 50 meters
- The length of the string (hypotenuse) = 70 meters

We can use the formula:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{50}{70}
\]

To find \(\theta\), we first calculate \(\sin(\theta)\):

\[
\sin(\theta) = \frac{50}{70} = \frac{5}{7} \approx 0.7143
\]

Now, to find the angle \(\theta\), we take the inverse sine (arcsin):

\[
\theta = \arcsin(0.7143)
\]

Using a calculator:

\[
\theta \approx 45.57°
\]

Therefore, the angle that the string makes with the ground is approximately **45.57°**.