Final answer:
Joe should place the foot of the 24-foot ladder approximately 11.36 feet away from the building so that the ladder reaches 20 feet up the building, with 1 foot of the ladder above the building.
Step-by-step explanation:
Joe wants to use a 24-foot ladder to reach the top of a 20-foot-tall building, with 1 foot of the ladder extending above the building's top. To find the distance from the foot of the ladder to the building, we can set up a right triangle, where the ladder is the hypotenuse. With the building acting as one leg (20 feet) and the unknown distance being the other leg, we apply the Pythagorean theorem: a^2 + b^2 = c^2.
Given that c = 23 feet (since 1 foot is above the building, it is not part of the hypotenuse in contact with the building) and b = 20 feet, we can calculate a (the distance from the ladder's foot to the building):
a^2 + 20^2 = 23^2
a^2 = 23^2 - 20^2
a^2 = 529 - 400
a^2 = 129
a = √129 ≈ 11.36 feet
Therefore, the foot of the ladder will be approximately 11.36 feet from the building.