To find the distance \( x \) between the foot of the ladder and the base of the building (adjacent side of the right triangle), we can use the cosine function. The cosine of the angle is defined as the ratio of the adjacent side to the hypotenuse in a right triangle.
Given:
- \( \text{Angle of elevation} = 55^\circ \)
- \( \text{Length of the ladder (hypotenuse)} = 16 \) ft
Using the cosine formula: \[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]
We can rewrite this as: \[ \cos(55^\circ) = \frac{x}{16} \]
Now, solve for \( x \): \[ x = 16 \cdot \cos(55^\circ) \]
Using a calculator: \[ \cos(55^\circ) \approx 0.5736 \]
Now plug this value in: \[ x = 16 \cdot 0.5736 \approx 9.1776 \]
Rounding this to the nearest hundredth: \[ x \approx 9.18 \text{ ft} \]
Therefore, the distance \( x \) between the foot of the ladder and the base of the building is \( \boxed{9.18 \text{ ft}} \).