No one needs to fix the window on the front door of our house. Bottom of the window is 16 feet in the ground she only has a 20 feet ladder how far from the base of the house she set up the ladder to the top of the ladder is exactly at the bottom of the window.
If the bottom of the window is 16 feet in the ground and the ladder is 20 feet long, the distance from the base of the house to where the ladder is set up can be determined using the Pythagorean theorem.
Let x be the distance from the base of the house to where the ladder is set up.
According to the theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. In this case, the ladder is the hypotenuse.
So, x^2 + 16^2 = 20^2
x^2 + 256 = 400
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides, x = √144
x = 12
Therefore, the distance from the base of the house to where the ladder is set up is 12 feet.
To determine the distance from the base of the house where the ladder should be set up, 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.
In this case, the ladder acts as the hypotenuse of the right triangle, and we need to find one of the other two sides.
Let's represent the distance from the base of the house to the ladder as "x." We know that the bottom of the window is 16 feet in the ground and the ladder is 20 feet long.
Using the Pythagorean theorem, we can set up the equation:
x^2 + 16^2 = 20^2
Simplifying this equation, we get:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 144
Taking the square root of both sides:
x = √144
Since both the positive and negative square roots of 144 are valid solutions, we have two possible values for x: +12 and -12. However, since we are looking for a distance, we consider only the positive value.
Thus, the ladder should be set up 12 feet from the base of the house to reach the bottom of the window, using a 20-foot ladder.
To find out how far from the base of the house the ladder should be placed, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder represents the hypotenuse, and we need to find the length of one of the other sides. Let's call the distance from the base of the house to where the ladder is set up "x" (in feet).
According to the problem, the bottom of the window is 16 feet in the ground, and the ladder is exactly at the bottom of the window. So, the vertical height the ladder needs to reach is 16 feet.
Using the Pythagorean theorem, we have:
x^2 + 16^2 = 20^2
Simplifying this equation, we get:
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 feet
Therefore, the ladder should be placed 12 feet from the base of the house in order to reach the bottom of the window.