To find the distance \( x \) from the base of the ladder to the wall, we can use trigonometry. The scenario can be represented as a right triangle, where:
- The hypotenuse is the length of the ladder (20 feet).
- The angle of elevation from the ground to the ladder is 50°.
- \( x \) is the adjacent side (the distance from the base of the ladder to the wall).
We will use the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Substituting the values into the equation:
\[ \cos(50°) = \frac{x}{20} \]
To solve for \( x \):
\[ x = 20 \cdot \cos(50°) \]
Now, we need to calculate \( \cos(50°) \):
Using a calculator:
\[ \cos(50°) \approx 0.6428 \]
Then, substituting this value back into the equation:
\[ x \approx 20 \cdot 0.6428 \approx 12.856 \]
Rounding to the nearest hundredth:
\[ x \approx 12.86 \text{ feet} \]
Thus, the distance from the base of the ladder to the wall is 12.86 feet.