A 45 foot ladder is set against the side of a house so that it reaches up 27 feet. If Cooper grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 23 ft .) Round to the nearest tenth of a foot.

To solve this, we can use the Pythagorean theorem. Initially, the ladder forms a right triangle where the ladder is the hypotenuse (45 ft), the height it reaches up the house is one leg (27 ft), and the distance from the base of the ladder to the house is the other leg. Using the Pythagorean theorem: 1. Find the original distance from the base of the ladder to the house: \(a^2 + b^2 = c^2\) where \(b = 27\) ft and \(c = 45\) ft. \(a^2 + 27^2 = 45^2\) \(a^2 + 729 = 2025\) \(a^2 = 2025 - 729\) \(a^2 = 1296\) \(a = \sqrt{1296} = 36\) ft. 2. Now, when Cooper pulls the ladder 4 ft farther away from the house, the new base distance is \(36 + 4 = 40\) ft. 3. Now, using the Pythagorean theorem again to find the new height (\(h\)): \(40^2 + h^2 = 45^2\) \(1600 + h^2 = 2025\) \(h^2 = 2025 - 1600\) \(h^2 = 425\) \(h = \sqrt{425} ≈ 20.7\) ft. So after pulling the ladder 4 feet farther from the house, it will reach approximately **20.7 feet** up the side of the house.