A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Shaniece grabs the ladder at its base and pulls it 10 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 38 ft.) Round to the nearest tenth of a foot
We can use the Pythagorean theorem to solve this problem. The ladder, the distance from the base to the house, and the height of the ladder form a right triangle.
Let's denote the distance from the base to the house as "x" and the height reached by the ladder as "h."
According to the Pythagorean theorem, we have:
x^2 + h^2 = 50^2
x^2 + 48^2 = 50^2
x^2 + 2304 = 2500
x^2 = 2500 - 2304
x^2 = 196
x = sqrt(196)
x = 14 ft
Initially, the ladder was set 48 ft up the house. After Shaniece pulls the ladder 10 ft farther from the house, the distance from the base to the house is now 14 ft + 10 ft = 24 ft.
Therefore, the ladder will reach 24 ft up the side of the house.