To find the distance \( x \) between the foot of the ladder and the base of the building, we can use the cosine function from trigonometry.
In this scenario, we can use the cosine of the angle of elevation:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
where:
- \( \theta = 55^\circ \) (the angle of elevation),
- the hypotenuse is the length of the ladder (16 feet),
- the adjacent side is the distance \( x \).
Now we can set up the equation:
\[ \cos(55^\circ) = \frac{x}{16} \]
To solve for \( x \), we can rearrange the equation:
\[ x = 16 \cdot \cos(55^\circ) \]
Now, we calculate \( \cos(55^\circ) \):
Using a calculator,
\[ \cos(55^\circ) \approx 0.5736 \]
Now we can compute \( x \):
\[ x \approx 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth:
\[ x \approx 9.18 \text{ ft} \]
Thus, the answer is:
x = 9.18 ft.