We can use trigonometry to solve this problem. Let's call the length of the ladder "L". Then, we can use the tangent function to relate the angle of elevation to the length of the ladder:
tan(63°) = opposite/adjacent
In this case, the "opposite" side is the height of the building that the ladder reaches, and the "adjacent" side is the distance between the base of the ladder and the building. We know that the distance between the base of the ladder and the building is 4 feet, so we can plug in the values we have:
tan(63°) = height/4
Now we can solve for the height:
height = 4 * tan(63°)
Using a calculator, we get:
height ≈ 8.32 feet
Therefore, the length of the ladder is approximately:
L = √(4^2 + 8.32^2) ≈ 9.38 feet
So the length of the ladder is approximately 9.38 feet.