To find the distance \( x \) from the base of the ladder to the building, you can use the sine function from trigonometry. The sine of the angle of elevation is defined as the opposite side (height against the wall) over the hypotenuse (the length of the ladder). However, you will use the cosine function to find the adjacent side, which is the distance \( x \).
The cosine function can be defined as:
\[ \cos(\theta) = \frac{\text{Adjacent side}}{\text{Hypotenuse}} \]
In this case:
- \( \theta = 46^\circ \)
- The hypotenuse (the length of the ladder) is \( 20 \) ft.
Thus, we can set up the equation:
\[ \cos(46^\circ) = \frac{x}{20} \]
Now, solve for \( x \):
\[ x = 20 \cdot \cos(46^\circ) \]
Now, calculate \( \cos(46^\circ) \):
Using a calculator:
\[ \cos(46^\circ) \approx 0.6947 \]
Thus,
\[ x \approx 20 \cdot 0.6947 \approx 13.894 \text{ ft} \]
Rounding it gives you \( x \approx 13.89 \) ft.
Therefore, the distance from the base of the ladder to the building is:
\[ \boxed{13.89 \text{ ft}} \]
So the correct answer is B. x=13.89 ft.