Question

Kyra is standing 50 feet from the kite she is flying. The string of the kite forms an angle of 27° with the ground. How high in the air is the kite? (1 point)
Responses

32.18 ft.
32.18 ft.

25.48 ft.
25.48 ft.

22.66 ft.
22.66 ft.

98.13 ft.

Answer 1

To determine how high the kite is in the air, we can use trigonometry. We can create a right triangle where:

- The length of the string is the hypotenuse (let's call it \( h \)).
- The height of the kite forms the opposite side of the angle.
- The distance from Kyra to the point directly below the kite on the ground forms the adjacent side (50 feet).

Using the sine function, we have:

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

In our case:

\[
\sin(27°) = \frac{\text{height of the kite}}{h}
\]

Since Kyra is standing 50 feet away from the kite, we can also find the hypotenuse \( h \) using the cosine function:

\[
\cos(27°) = \frac{50 \text{ ft}}{h}
\]

Now we can rearrange this to find \( h \):

\[
h = \frac{50}{\cos(27°)}
\]

Calculating \( \cos(27°) \):

\[
h = \frac{50}{\cos(27°)} \approx \frac{50}{0.8480} \approx 58.9 \text{ ft}
\]

Now, substituting \( h \) back to find the height of the kite:

\[
\sin(27°) = \frac{\text{height}}{58.9}
\]
\[
\text{height} = 58.9 \times \sin(27°)
\]
Calculating \( \sin(27°) \):

\[
\text{height} = 58.9 \times 0.4540 \approx 26.68 \text{ ft}
\]

Since this is not one of the options given, let's go back and use the direct calculation from the 50 feet distance:

Using the triangle:

\[
\text{height} = 50 \times \tan(27°)
\]

Calculating \( \tan(27°) \):

\[
\tan(27°) \approx 0.510
\]

Now:

\[
\text{height} \approx 50 \times 0.510 \approx 25.5 \text{ ft}
\]

So, the height of the kite is approximately 25.48 feet, which corresponds to one of the given options.

Therefore, the answer is:

**25.48 ft.**