Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has a 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window? (1 point)
To solve this problem, we can use the Pythagorean theorem. Let x be the distance from the base of the ladder to the base of the house, and let y be the height of the ladder needed to reach the bottom of the window.
According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
In this case, we have a right triangle with a leg of length x, a leg of length y, and a hypotenuse of length 20 ft.
Therefore, we can write the equation:
x^2 + y^2 = 20^2
Since the bottom of the window is 16 ft. from the ground, the height of the ladder needed is y = 16 ft.
Substituting y = 16 ft. into the equation, we have:
x^2 + (16 ft.)^2 = 20^2
x^2 + 256 ft.^2 = 400 ft.^2
x^2 = 400 ft.^2 - 256 ft.^2
x^2 = 144 ft.^2
x = √144 ft.
x = 12 ft.
Therefore, Camila should set up the ladder 12 ft. from the base of the house.