To find the distance \( x \) between the foot of the ladder and the base of the building, we can use the cosine function in a right triangle formed by the ladder, the wall, and the ground.
In this triangle:
- The hypotenuse is the length of the ladder, which is 16 feet.
- The angle of elevation is 55°.
- \( x \) (the distance from the foot of the ladder to the base of the building) is the adjacent side.
According to the cosine definition:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In our case, this means:
\[ \cos(55°) = \frac{x}{16} \]
To solve for \( x \), we rearrange the equation:
\[ x = 16 \cdot \cos(55°) \]
Using a calculator to find \( \cos(55°) \):
\[ \cos(55°) \approx 0.5736 \]
Now, substitute this value into the equation:
\[ x = 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth gives:
\[ x \approx 9.18 \text{ ft} \]
Therefore, the correct answer is:
x = 9.18 ft.