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)
bl
She should set up the ladder 4 ft. away from the base of the house.
Wromg
My apologies for the incorrect response. To determine the correct distance from the base of the house to set up the ladder, we can use the Pythagorean theorem.
Let's denote the distance from the base of the house to the desired position of the ladder as x. The height of the ladder is 20 ft., and the height from the ground to the bottom of the window is 16 ft.
According to the Pythagorean theorem, (base)^2 + (height)^2 = (hypotenuse)^2, so (x)^2 + (16)^2 = (20)^2.
Simplifying the 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 have x = ±12.
Since we are measuring distance, it must be positive, so x = 12 ft.
Therefore, Camila should set up the ladder 12 ft. away from the base of the house.
To determine how far from the base of the house Camila should set up the ladder, we can use the Pythagorean theorem.
According to the theorem, the square of the hypotenuse (the length of the ladder) is equal to the sum of the squares of the other two sides (the height of the window from the ground and the distance from the base of the ladder to the house).
Let's denote the distance from the base of the ladder to the house as x. We know that the height of the window from the ground is 16 ft and the length of the ladder is 20 ft.
Therefore, using the Pythagorean theorem, we can write:
x^2 + 16^2 = 20^2
Simplifying this equation:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 144
Taking the square root of both sides:
x = √144
So, Camila should set up the ladder approximately 12 ft from the base of the house in order to align the top of the ladder with the bottom of the window.