Final answer:
Using the Pythagorean theorem, initially 14 feet away from the house, after being pulled out 6 additional feet to 20 feet from the base, the ladder will reach approximately 45.83 feet up the side of the house.
Step-by-step explanation:
The question involves finding how far up the side of the house a ladder will reach after being moved. Initially, the ladder reaches 48 feet up the side of a house and is then pulled 6 feet farther from the house's base. We can use the Pythagorean theorem to solve this problem as it involves a right triangle formed by the ladder, the wall of the house, and the ground.
Let's denote the original distance from the house as x and the new distance as x + 6 feet. The ladder's length L remains constant at 50 feet. We are given the initial height H reached by the ladder as 48 feet. The new height h is what we need to find.
The Pythagorean theorem tells us that L^2 = H^2 + x^2 initially, and after being moved, L^2 = h^2 + (x + 6)^2. Solving these two equations gives us the new height h that the ladder will reach.
- First, find x using the initial conditions: x^2 = L^2 - H^2.
- Then, plug this value into the second equation to solve for h.
Let's find x:
x^2 = L^2 - H^2 = 50^2 - 48^2 = 2500 - 2304 = 196
So, x = √196 = 14 feet.
Now solve for h:
h^2 = L^2 - (x + 6)^2 = 50^2 - (14 + 6)^2 = 2500 - 400 = 2100
h = √2100 ≈ 45.83 feet.
Therefore, after being pulled 6 feet farther from the house, the ladder will reach approximately 45.83 feet up the side of the house.