While painting the side of his house, Jason positioned his ladder so that the top was 16 feet above the ground, while the bottom was 12 feet away from the base of the wall. To reach a spot higher up on the house, Jason moved the ladder so that the top was 18 feet above the ground. How much closer to the house is the bottom of the ladder now? If nec ssary, round your answer to the nearest tenth. Submit

To solve this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the height and the distance from the wall). Initially, when the top of the ladder is 16 feet high and the bottom is 12 feet away, we have: \(L_1^2 = 16^2 + 12^2\) \(L_1^2 = 256 + 144 = 400\) \(L_1 = \sqrt{400} = 20\) feet (the length of the ladder). Now, when Jason moves the ladder so that the top is 18 feet high, we can find the new distance from the wall using the same theorem: Let \(d\) be the new distance from the wall: \(L_2^2 = 18^2 + d^2\) \(20^2 = 324 + d^2\) \(400 = 324 + d^2\) \(d^2 = 400 - 324 = 76\) \(d = \sqrt{76} \approx 8.7\) feet. Now, to find out how much closer to the wall Jason has moved the ladder: Original distance = 12 feet, New distance ≈ 8.7 feet. Difference: \(12 - 8.7 = 3.3\) feet. So, the bottom of the ladder is approximately 3.3 feet closer to the house.