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

22.66 ft.
22.66 ft.

25.48 ft.
25.48 ft.

32.18 ft.
32.18 ft.

98.13 ft.

Answer 1

To find the height of the kite, we can use some trigonometry. We know the distance from Kyra to the base of the kite (50 feet) and the angle of the string with the ground (27°). The height of the kite can be found using the sine function.

The sine of an angle in a right triangle is defined as the opposite side (height of the kite) divided by the hypotenuse (length of the string). To find the height (h), we can set up the equation:

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

In this case, the opposite side is the height of the kite (h), and we need to find the length of the string (hypotenuse) first using cosine:

\[
\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

So, we can find the hypotenuse (length of string) as:

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

Now, plug this hypotenuse back into the sine function to find the height:

\[
h = \text{hypotenuse} \cdot \sin(27°)
\]

Calculating the hypotenuse first:

\[
\cos(27°) \approx 0.848
\]
\[
\text{hypotenuse} = \frac{50}{0.848} \approx 59.01 \text{ feet}
\]

Now using this to find the height:

\[
h = 59.01 \cdot \sin(27°)
\]
\[
\sin(27°) \approx 0.454
\]
\[
h \approx 59.01 \cdot 0.454 \approx 26.81 \text{ feet}
\]

This means the kite's height is about 26.81 feet.

However, we can also find the height directly without calculating the string length:

Using the relationship directly:

\[
h = 50 \cdot \tan(27°)
\]

Calculating this gives:

\[
\tan(27°) \approx 0.509
\]
\[
h \approx 50 \cdot 0.509 \approx 25.45 \text{ feet}
\]

So the closest match from your provided options would be **25.48 ft.**