A 12 foot ladder is leaning against a house. If the top of the ladder reaches 8 feet up the house, how far is the bottom of the ladder from the base of the house?
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This is a straightforward Pythagoras question
x^2 + 8^2 = 12^2
I got 8.94 correct to 2 decimals
it is 8.94
What’s the answer?
To find the distance from the base of the house to the bottom of the ladder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, which is the hypotenuse.
In this case, the ladder is the hypotenuse, the height of the house is one of the shorter sides, and the distance we want to find is the other shorter side.
Let's denote the distance from the base of the house to the bottom of the ladder as "x". According to the problem, the height of the house is 8 feet, and the length of the ladder is 12 feet.
Using the Pythagorean theorem, we can set up the following equation:
x^2 + 8^2 = 12^2
Simplifying the equation, we have:
x^2 + 64 = 144
Subtracting 64 from both sides:
x^2 = 80
Now, we can take the square root of both sides to solve for x:
√(x^2) = √80
x = √80
Calculating the square root of 80, we find that x is approximately 8.94 feet.
Therefore, the bottom of the ladder is approximately 8.94 feet from the base of the house.