To find the height of the kite above the ground, we can use the sine function from trigonometry. The sine function relates the angle of a right triangle to the ratio of the opposite side (height of the kite) to the hypotenuse (length of the string).
In this case:
- The adjacent side (distance from Kyra to the base of the kite) is 50 feet.
- The angle is 27°.
We can use the following formula:
\[ \text{Height} = \text{hypotenuse} \cdot \sin(\text{angle}) \]
However, we don't know the length of the string (hypotenuse). To find it, we can use the cosine function, since we know the adjacent side.
\[ \cos(27°) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \Rightarrow \text{Hypotenuse} = \frac{\text{Adjacent}}{\cos(27°)} \]
First, let's calculate the hypotenuse:
\[ \text{Hypotenuse} = \frac{50}{\cos(27°)} \]
Next, we can find the height using the sine function.
\[ \text{Height} = \text{Hypotenuse} \cdot \sin(27°) \]
Calculating the cosine and sine values:
- Calculate \( \cos(27°) \) and \( \sin(27°) \):
- \( \cos(27°) \approx 0.846 \)
- \( \sin(27°) \approx 0.454 \)
Now calculate the hypotenuse:
\[ \text{Hypotenuse} = \frac{50}{0.846} \approx 59.06 \text{ feet} \]
Now calculate the height:
\[ \text{Height} = 59.06 \cdot 0.454 \approx 26.83 \text{ feet} \]
This does not seem to match any provided options. However, if we instead use the tangent function for the height directly, since we know the opposite and adjacent sides:
\[ \tan(27°) = \frac{\text{Height}}{50} \Rightarrow \text{Height} = 50 \cdot \tan(27°) \]
Calculating \( \tan(27°) \):
- \( \tan(27°) \approx 0.510 \)
Now calculate the height:
\[ \text{Height} = 50 \cdot 0.510 \approx 25.50 \text{ feet} \]
This rounded value is closest to 25.48 ft.
Thus, the height of the kite is approximately 25.48 ft.