To find the distance \( x \) from the base of the ladder to the wall, we can use trigonometry. Specifically, we can use the cosine function, since we know the length of the ladder and the angle of elevation.
The cosine of the angle is defined as:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case, the adjacent side is the distance \( x \) we want to find, and the hypotenuse is the length of the ladder (15 feet).
We can set up the equation:
\[ \cos(33°) = \frac{x}{15} \]
Now, we can solve for \( x \):
\[ x = 15 \cdot \cos(33°) \]
Using a calculator to find \( \cos(33°) \):
\[ \cos(33°) \approx 0.8387 \]
Now substitute this value back into the equation:
\[ x \approx 15 \cdot 0.8387 \approx 12.5805 \]
Rounding to the nearest hundredth, we get:
\[ x \approx 12.58 \text{ feet} \]
Thus, the correct answer is:
12.58 feet