Final answer:
Using the Pythagorean theorem, we can determine that a 25-foot ladder leaning against a building with its base 7 feet from the building touches the building at a height of 24 feet above the ground.
Step-by-step explanation:
The question is asking to determine how high up the ladder reaches on the building. To find this, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem can be written as c2 = a2 + b2, where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In this scenario, the ladder represents the hypotenuse of the triangle (c), the distance from the base of the building to the base of the ladder represents one side (a), and the height at which the ladder touches the building is the second side (b). We are given that c = 25 feet (the length of the ladder) and a = 7 feet (the distance the ladder is from the building).
We can rearrange the Pythagorean theorem to solve for b: b2 = c2 - a2. Plugging in the given values, we have b2 = 252 - 72 = 625 - 49 = 576. Taking the square root of both sides, we find that b = √576 = 24 feet. Therefore, the ladder touches the building at a height of 24 feet above the ground.