To determine how many feet up the apartment building the top of the ladder reaches, we can use the Pythagorean theorem. The ladder forms a right triangle where:
- The ladder is the hypotenuse (c), which is 41 feet.
- The distance from the base of the ladder to the wall is one leg (a), which is 9 feet.
- The height up the wall (b) is the other leg we want to find.
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Substituting the values we have:
\[ 9^2 + b^2 = 41^2 \]
Calculating the squares:
\[ 81 + b^2 = 1681 \]
Now, solving for \( b^2 \):
\[ b^2 = 1681 - 81 \] \[ b^2 = 1600 \]
Taking the square root of both sides gives us:
\[ b = \sqrt{1600} \] \[ b = 40 \]
Thus, the top of the ladder reaches 40 feet up the apartment building.
The answer is A. 40 feet.