Camila needs to fix the window on the front of her house. The bottom of the window is 16 feet from the ground. She only has a 20 foot ladder how far from the base of the house she set up the ladder so that the top of the ladder is exactly at the bottom of the window.
To set up the ladder so that the top is exactly at the bottom of the window, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's denote the distance from the base of the house to the point where the ladder touches the ground as x. We need to find the value of x.
According to the problem, the bottom of the window is 16 feet from the ground. Therefore, the vertical distance from the base of the ladder to the bottom of the window is also 16 feet.
We can set up the following equation using the Pythagorean theorem:
x^2 + 16^2 = 20^2
Simplifying this equation, we have:
x^2 + 256 = 400
Subtracting 256 from both sides, we get:
x^2 = 144
Taking the square root of both sides, we find:
x = ±12
Since x represents a distance, it cannot be negative. Therefore, we conclude that x = 12.
Therefore, Camila needs to set up the ladder 12 feet from the base of the house to align the top of the ladder exactly with the bottom of the window.