Final answer:
Camila should set up her ladder 12 feet away from the base of her house to reach the bottom of the window 16 feet off the ground with her 20-foot ladder, using the Pythagorean theorem.
Step-by-step explanation:
To calculate how far from the base of the house Camila should set up her ladder so that the top reaches the bottom of the window, we use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the ladder will form the hypotenuse, the distance from the ground up to the window will be one side, and the distance from the base of the house to the bottom of the ladder will be the other side. We have the length of the ladder (hypotenuse) as 20 ft and the height up to the window (one side) as 16 ft.
Using the Pythagorean theorem, we can write the equation as:
Ladder^2 = Height^2 + Distance^2
Where:
- Ladder is the length of the ladder
- Height is the height from the ground to the bottom of the window
- Distance is the distance from the base of the house to the ladder
Substituting the values we have into the equation:
20^2 = 16^2 + Distance^2
Distance^2 = 20^2 - 16^2
Distance^2 = 400 - 256
Distance^2 = 144
Distance = √144
Distance = 12 ft
So, Camila should set up her ladder 12 feet away from the base of her house.