Final answer:
The length of the ladder can be found using the Pythagorean theorem, where we calculate the hypotenuse of the right triangle formed by the ladder, the building, and the ground. The ladder is 25 feet long.
Step-by-step explanation:
To determine the length of the ladder, we can use the Pythagorean theorem, which is a formula used to find the length of the sides of a right triangle. The formula is c2 = a2 + b2, where c represents the length of the hypotenuse (the longest side of the right triangle opposite the right angle), and a and b are the lengths of the other two sides.
In this problem, the base of the ladder is 7 feet from the building and the ladder reaches 24 feet up the building. Here, 7 feet is one side (a) and 24 feet is the other side (b) of the right triangle formed by the building, the ground, and the ladder. We are looking for the length of the ladder, which corresponds to the hypotenuse c.
Let's use the Pythagorean theorem to calculate:
- a2 = 72 = 49
- b2 = 242 = 576
- c2 = a2 + b2 = 49 + 576 = 625
- c = √625 = 25
The length of the ladder is 25 feet, so the correct answer is (a) 25.0 feet.