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