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?
To find the distance between the base of the ladder and the house, we can use the Pythagorean theorem.
Let's assume the distance from the base of the ladder to the house is 'x' feet.
According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
In this case, one leg represents the vertical height of the house (12 feet) and the other leg represents the distance from the base of the ladder to the house ('x' feet). The hypotenuse represents the length of the ladder (20 feet).
So, the equation would be: x^2 + 12^2 = 20^2.
Simplifying the equation: x^2 + 144 = 400.
Rearranging the equation: x^2 = 400 - 144.
x^2 = 256.
Taking the square root of both sides: x = 16.
Therefore, the base of the ladder is 16 feet away from the house.
To determine the distance from the house to the base of the ladder, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the ladder forms the hypotenuse of a right triangle, with the height of the house being one side and the distance from the house to the ladder base being the other side.
Using the formula, we can find the distance from the house to the ladder base:
Distance from the house to the ladder base = √[(h^2) - (l^2)]
Where:
h = Height of the house = 12 feet
l = Length of the ladder = 20 feet
Plugging in the values, we get:
Distance from the house to the ladder base = √[(12^2) - (20^2)]
= √[144 - 400]
= √[-256]
Since the result is √[-256], it means that the ladder is not long enough to reach the gutters.
To find out how far away from the house the base of the ladder is, we can use the Pythagorean theorem. The Pythagorean theorem 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, the ladder is the hypotenuse, and the height of the house is one of the other two sides. The distance from the base of the ladder to the house is the remaining side.
Let's denote the distance from the base of the ladder to the house as 'x'. We have the equation:
x^2 + 12^2 = 20^2
Simplifying:
x^2 + 144 = 400
Subtracting 144 from both sides:
x^2 = 256
Taking the square root of both sides:
x = √256
Since the distance cannot be negative, the solution is x = 16.
Therefore, the base of the ladder is 16 feet away from the house.