How long is a ladder that reaches a window 17 feet above the ground with its base 5 feet away from the wall?

To determine the length of the ladder required to reach a window 17 feet above the ground, while its base is positioned 5 feet away from the wall, we can apply the Pythagorean theorem. This theorem is essential for calculating the length of the hypotenuse in a right triangle, which in this case is represented by the ladder.

In this scenario, the height from the ground to the window serves as one leg of the triangle, measuring 17 feet. The distance from the base of the ladder to the wall constitutes the second leg, measuring 5 feet. According to the Pythagorean theorem, which states that the square of the hypotenuse (the ladder's length) is equal to the sum of the squares of the other two sides, we can formulate our calculation as follows:

1. Square the height (17 feet): (17^2 = 289)

2. Square the distance from the wall (5 feet): (5^2 = 25)

3. Add these two results: (289 + 25 = 314)

4. Take the square root to find the length of the ladder: (\sqrt{314} \approx 17.7) feet, or