To solve for \( x \), the distance from the foot of the ladder to the base of the wall, we can use the cosine of the angle of elevation. The cosine function is defined as:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case:
- \(\theta = 55^\circ\)
- The adjacent side is \( x \) (the distance from the wall)
- The hypotenuse is the length of the ladder, which is 16 feet.
Thus, we can write the equation:
\[ \cos(55^\circ) = \frac{x}{16} \]
Now, we can solve for \( x \):
\[ x = 16 \cdot \cos(55^\circ) \]
Now we can calculate \( \cos(55^\circ) \):
Using a calculator:
\[ \cos(55^\circ) \approx 0.5736 \]
Now substitute this value into the equation for \( x \):
\[ x = 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth:
\[ x \approx 9.18 , \text{ft} \]
Therefore, the correct response is:
x = 9.18 ft.