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)
ft.
THE ANSWER IS NOT 4!
To determine the distance from the base of the house where Camila should set up the ladder, we can use the Pythagorean theorem.
Let's assume that the distance from the base of the house to the desired setup point of the ladder is x ft. The height of the ladder can be considered as 20 ft, and the distance of 16 ft is the vertical distance from the ground to the bottom of the window.
According to the Pythagorean theorem, the square of the hypotenuse (20 ft ladder) is equal to the sum of the squares of the other two sides (x ft distance from the base) and 16 ft.
Therefore, we have the equation:
x^2 + 16^2 = 20^2
Simplifying this equation further:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides:
x = √144
x = 12 ft
So, Camila should set up the ladder approximately 12 ft from the base of the house to align the top of the ladder with the bottom of the window.
To solve this problem, we can use the Pythagorean theorem. The ladder acts as the hypotenuse of a right triangle, with the distance from the base of the ladder to the house as one leg, and the distance from the house to the bottom of the window as the other leg.
Let's call the distance from the base of the ladder to the house "x".
According to the problem, the distance from the bottom of the window to the ground is 16 ft. The distance from the bottom of the window to the base of the ladder can be found by subtracting 16 ft from the length of the ladder. So, it would be (20 ft - 16 ft) = 4 ft.
Using the Pythagorean theorem, we have:
x^2 + 4^2 = 20^2
Simplifying:
x^2 + 16 = 400
Subtracting 16 from both sides:
x^2 = 384
Taking the square root of both sides:
x =~19.6
So, she should set up the ladder approximately 19.6 ft from the base of the house.
To find out how far from the base of the house Camila should set up the ladder, we can use the concept of similar triangles.
Let's assume the distance from the base of the ladder to the base of the window is x ft. Now, we have two similar right triangles - one formed by the ladder, the ground, and the distance x, and the other formed by the window, the ground, and the distance 16 ft.
Since the two triangles are similar, their corresponding sides are in proportion. We can set up the following proportion:
(Length of ladder)/(Distance on ground) = (Length of window)/(Distance from ladder base to window base)
Substituting the given values, we have:
20 ft./x ft. = 16 ft./16 ft.
Simplifying the above equation:
20/x = 16/16
20/x = 1
20 = x
Therefore, Camila should set up the ladder 20 ft. from the base of the house so that the top of the ladder is exactly at the bottom of the window.