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Answer:
Step-by-step explanation:
To find the height of the kite, we can use trigonometry, specifically the sine function, since we have the angle of elevation and the length of the string (which acts as the hypotenuse of a right triangle formed with the ground).
Given:
- Angle of elevation (\( \theta \)) = 25°
- Length of the string (hypotenuse) = 100 ft
Let \( h \) denote the height of the kite above the ground.
According to trigonometry:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
\[ \sin(25^\circ) = \frac{h}{100} \]
Now, solve for \( h \):
\[ h = 100 \cdot \sin(25^\circ) \]
Calculate \( \sin(25^\circ) \):
\[ \sin(25^\circ) \approx 0.4226 \]
Now, calculate \( h \):
\[ h \approx 100 \cdot 0.4226 \]
\[ h \approx 42.26 \]
Rounded to the nearest hundredth, the height of the kite is approximately \( \boxed{42.26} \) feet.