To find the distance \( x \) between the foot of the ladder and the base of the building using cosine, you can use the cosine function defined in a right triangle:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case, \( \theta = 55^\circ \), the hypotenuse (the length of the ladder) is 16 feet, and the adjacent side is \( x \).
Using the cosine formula, we have:
\[ \cos(55^\circ) = \frac{x}{16} \]
To solve for \( x \), multiply both sides by 16:
\[ x = 16 \cdot \cos(55^\circ) \]
Now, let's calculate \( \cos(55^\circ) \):
\[ \cos(55^\circ) \approx 0.5736 \]
Now substitute back to find \( x \):
\[ x \approx 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth, we get:
\[ x \approx 9.18 , \text{ft} \]
Thus, the answer is:
x equals 9.18 ft.