Questions: vveek 9 Discussion A 17-foot ladder reaches a window 15 feet above the ground. How far from the wall is the base of the ladder? Reply - Previous

Solution Steps

To find how far the base of the ladder is from the wall, we can use the Pythagorean theorem. The ladder forms the hypotenuse of a right triangle, with the distance from the wall and the height of the window as the other two sides. By applying the Pythagorean theorem, we can solve for the distance from the wall.

The problem involves a right triangle formed by the ladder, the wall, and the ground. The ladder acts as the hypotenuse, the height of the window is one leg, and the distance from the wall is the other leg.

The Pythagorean theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), the relationship is given by: \[ a^2 + b^2 = c^2 \] In this problem, the hypotenuse \(c\) is 17 feet, and one leg \(b\) (the height of the window) is 15 feet. We need to find the other leg \(a\) (the distance from the wall).

Rearrange the Pythagorean theorem to solve for \(a\): \[ a = \sqrt{c^2 - b^2} \] Substitute the known values: \[ a = \sqrt{17^2 - 15^2} = \sqrt{289 - 225} = \sqrt{64} = 8.0 \]

Final Answer