Final answer:
Using the Pythagorean theorem, it is calculated that a 25-foot ladder with its base 15 feet away from a wall will only reach up to 20 feet high on the wall. Thus, the ladder will not reach a window that is 21.5 feet above the ground.
Step-by-step explanation:
The student's question involves determining if a ladder of a certain length can reach a particular height when leaned against a wall at a given distance from the base. This problem is a classic application of the Pythagorean theorem and can be categorized under high school-level Mathematics. The theorem 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.
To solve this problem, let the length of the ladder be the hypotenuse c, the height the ladder reaches up the wall be a, and the distance from the wall to the base of the ladder be b. Using the Pythagorean theorem, we can express this relationship as:
a2 + b2 = c2
Given c = 25 feet (ladder length), b = 15 feet (distance from the wall), let's calculate the height a that the ladder can reach up the wall:
a2 = c2 - b2
a2 = 252 - 152
a2 = 625 - 225
a2 = 400
a = √400
a = 20 feet
Since the window is at 21.5 feet, which is higher than 20 feet, the ladder will not reach the window.