To solve for the distance \( x \) between the foot of the ladder and the base of the building, we can use the cosine of the angle.
Given:
- The length of the ladder (hypotenuse) = 16 feet
- The angle of elevation \( \theta = 55^\circ \)
The cosine of an angle in a right triangle is defined as the adjacent side (in this case, \( x \)) over the hypotenuse:
\[ \cos(\theta) = \frac{x}{\text{hypotenuse}} \]
Now, substituting the values we have:
\[ \cos(55^\circ) = \frac{x}{16} \]
To find \( x \), we can rearrange the equation:
\[ x = 16 \cdot \cos(55^\circ) \]
Now, calculating \( \cos(55^\circ) \) (in degrees):
Using a calculator:
\[ \cos(55^\circ) \approx 0.5736 \]
Now substitute this value back into the equation for \( x \):
\[ x \approx 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth:
\[ x \approx 9.18 \]
Thus, the distance between the foot of the ladder and the base of the building is approximately 9.18 feet.