Final answer:
Using the Pythagorean theorem, the length of the ladder needed to reach a window 45 feet above the ground, with the base of the ladder 18 feet from the building, is approximately 48.47 feet. The nearest whole number for the ladder's length is 49 feet (choice c).
Step-by-step explanation:
To determine the length of a ladder needed to reach a window 45 feet above the ground, we can use the Pythagorean theorem. This 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. In this case, the ladder will act as the hypotenuse, the distance from the base of the ladder to the building is one side, and the height of the window from the ground is the other side.
Given that the base of the ladder is 18 feet from the building (one side of the triangle) and the window is 45 feet above the ground (the other side of the triangle), we can set up the equation:
Ladder length2 = Base2 + Height2
Ladder length2 = 182 + 452
Ladder length2 = 324 + 2025
Ladder length2 = 2349
Ladder length = √2349
Ladder length ≈ 48.47 feet
Therefore, the nearest whole number for the ladder length needed is 49 feet, which is choice (c).