To solve for the distance \( x \) between the foot of the ladder and the base of the building, we can use the cosine function. The cosine of the angle of elevation is defined as the ratio of the adjacent side (the distance from the foot of the ladder to the building) to the hypotenuse (the length of the ladder).
Given:
- Length of the ladder (hypotenuse) = 16 feet
- Angle of elevation = 55°
Using the cosine formula:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
We can rearrange it to solve for the adjacent side \( x \):
\[ x = \text{hypotenuse} \cdot \cos(\theta) = 16 \cdot \cos(55^\circ) \]
Now, calculating \( \cos(55^\circ) \):
\[ \cos(55^\circ) \approx 0.5736 \]
Now plug the value back into the equation:
\[ x = 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth, we get:
\[ x \approx 9.18 \text{ ft} \]
Thus, the correct response is:
x equals 9.18 ft.