To find the distance \( x \) between the foot of the ladder and the base of the building, we can use the cosine function.
The cosine of an angle in a right triangle is defined as the ratio of the adjacent side (which is \( x \) in this case) to the hypotenuse (the length of the ladder).
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case:
- \( \theta = 55^\circ \)
- The hypotenuse (length of the ladder) = 16 feet.
The formula becomes:
\[ \cos(55^\circ) = \frac{x}{16} \]
To find \( x \), we can rearrange the equation:
\[ x = 16 \cdot \cos(55^\circ) \]
Now, we calculate \( \cos(55^\circ) \):
\[ \cos(55^\circ) \approx 0.5736 \]
Now we can find \( x \):
\[ x \approx 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth:
\[ x \approx 9.18 \text{ ft} \]
Thus, the correct answer is:
x equals 9.18 ft.
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