To find the height of the kite, we can use the sine function from trigonometry. The height of the kite can be represented as the opposite side of a right triangle, where the distance from Kyra to the kite (50 feet) is the adjacent side.
We can use the sine function, which is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \( \theta \) is the angle of 27 degrees, the opposite side is the height of the kite (let’s call it \( h \)), and the hypotenuse is the length of the string.
We can find the height using the tangent function instead:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Plugging in our values:
\[ \tan(27^\circ) = \frac{h}{50} \]
To find the height (\( h \)), we rearrange this equation:
\[ h = 50 \cdot \tan(27^\circ) \]
Now we calculate \(\tan(27^\circ)\):
\[ \tan(27^\circ) \approx 0.5108 \]
Now substituting this value back into the equation:
\[ h \approx 50 \cdot 0.5108 \approx 25.54 \]
Thus, the height of the kite, rounded to the nearest hundredth, is approximately:
\[ \boxed{25.54} \text{ feet} \]
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