You are cleaning the gutters out of your house which stands 12 feet tall. You are using a ladder that is 20 feet long to reach the gutters. How far away from the house is the base of the ladder?
a2+b2=c2
A basic visual for the word problem. The ladder is represented by the 20 units diagonal and the house represented by the 12 units side. (10 points)
The ladder is
feet away from the house
To find the distance from the base of the ladder to the house, we can use the Pythagorean theorem. Let's call the distance from the base of the ladder to the house "x". According to the Pythagorean theorem:
a^2 + b^2 = c^2
where:
a = distance from the base of the ladder to the house (x)
b = height of the house (12 ft)
c = length of the ladder (20 ft)
Substituting the given values into the equation, we get:
x^2 + 12^2 = 20^2
Simplifying the equation, we have:
x^2 + 144 = 400
Subtracting 144 from both sides:
x^2 = 256
Taking the square root of both sides:
x = √256
x = 16
So, the base of the ladder is 16 feet away from the house.
To find the distance of the base of the ladder from the house, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder represents the hypotenuse of the right triangle, and the distance from the base of the ladder to the house represents one of the other sides.
Using the formula a^2 + b^2 = c^2, where a and b are the lengths of the other two sides and c is the length of the hypotenuse, we can solve for the distance of the base of the ladder from the house.
Here, the length of the ladder (c) is 20 feet and the height of the house (a) is 12 feet. Let's plug these values into the formula:
12^2 + b^2 = 20^2
144 + b^2 = 400
Now, let's solve for b by subtracting 144 from both sides of the equation:
b^2 = 400 - 144
b^2 = 256
Taking the square root of both sides, we find:
b = √256
b = 16
Therefore, the distance of the base of the ladder from the house is 16 feet.
To determine the distance between the base of the ladder and the house, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with one side measuring 12 feet (the height of the house) and the hypotenuse measuring 20 feet (the length of the ladder). Let's assume the distance between the base of the ladder and the house is x feet.
So, according to the Pythagorean theorem, we have the equation:
12^2 + x^2 = 20^2
Simplifying, we have:
144 + x^2 = 400
Subtracting 144 from both sides:
x^2 = 256
Taking the square root of both sides to solve for x:
x = √256
x = 16
Therefore, the base of the ladder is 16 feet away from the house.