To solve this problem, we can use the Pythagorean theorem. The ladder, the height of the building, and the distance from the bottom of the ladder to the building form a right triangle.
Here, we can define:
- The length of the ladder (hypotenuse) as \( c = 32 \) feet,
- The height of the building (one leg of the triangle) as \( a = 23 \) feet,
- The distance from the bottom of the ladder to the building (the other leg of the triangle) as \( b \).
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Substituting the values we know:
\[ 23^2 + b^2 = 32^2 \]
Calculating the squares:
\[ 529 + b^2 = 1024 \]
Now, subtract 529 from both sides:
\[ b^2 = 1024 - 529 \] \[ b^2 = 495 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{495} \]
Calculating \( \sqrt{495} \):
\[ \sqrt{495} \approx 22.3 \]
Thus, the distance from the bottom of the ladder to the building is approximately 22.3 feet, when rounded to the nearest tenth of a foot.