To find the distance \( x \) between the foot of the ladder and the base of the building using the cosine function, we can use the cosine of the angle of elevation.
The cosine function relates the adjacent side (distance from the wall, \( x \)) to the hypotenuse (the length of the ladder):
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Here, \( \theta = 55^\circ \) and the hypotenuse is the length of the ladder, which is 16 feet. Therefore, we have:
\[ \cos(55^\circ) = \frac{x}{16} \]
To solve for \( x \), we can rearrange the equation:
\[ x = 16 \cdot \cos(55^\circ) \]
Now we can calculate:
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Find \( \cos(55^\circ) \):
- Using a calculator, \( \cos(55^\circ) \approx 0.5736 \).
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Now calculate \( x \): \[ x = 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth, we get:
\[ x \approx 9.18 \text{ ft.} \]
Thus, the correct answer is:
x = 9.18 ft.