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.
To solve this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Here, the ladder represents the hypotenuse, the distance from the base of the ladder to the bottom of the window is one side, and the distance from the base of the ladder to the ground is the other side. Let's call the distance from the base of the ladder to the ground "x".
Using the Pythagorean theorem, we can set up the equation:
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
Therefore, Camila should set up the ladder 12 feet away from the base of the house.
12 ft :)
To solve this problem, we can use the concept of similar triangles.
In the given scenario, we have a right triangle formed by the ladder, the ground, and the line connecting the base of the ladder to the window. Let's call the distance from the base of the house to the ladder x ft.
We know that the bottom of the window is 16 ft high, and the ladder is 20 ft long. Therefore, we can set up a proportion:
x / 16 = (20 - x) / 20
To solve this proportion, we can cross-multiply:
20x = 16(20 - x)
Expanding both sides:
20x = 320 - 16x
Combining like terms:
36x = 320
Dividing by 36:
x = 320 / 36
Simplifying:
x ≈ 8.8889 ft
Therefore, Camila should set up the ladder approximately 8.8889 ft from the base of the house.