I need a bit of help on this question: a nine foot long ladder is leaned against a house, reaching a point seven feet above the ground. How far from the house is the base of the ladder? Please help!
remember your Pythagorean Theorem?
x^2 + 7^2 = 9^2
Now just find x
Sure, I can help you with that question!
To find out how far 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 (in this case, the ladder) is equal to the sum of the squares of the other two sides.
In this problem, the ladder is the hypotenuse, and the two sides of the right triangle are the height of the ladder (7 feet) and the distance from the house to the base of the ladder (which we want to find).
Let's call the distance from the house to the base of the ladder "x" feet.
Using the Pythagorean theorem, we can set up the equation:
x^2 + 7^2 = 9^2
To solve this equation, we first square the known values:
x^2 + 49 = 81
Then, we subtract 49 from both sides of the equation:
x^2 = 81 - 49
Simplifying further:
x^2 = 32
To isolate x, we take the square root of both sides of the equation:
√(x^2) = √32
x = √32
Now, we can simplify the square root of 32 as 5.657, approximately.
So, the distance from the house to the base of the ladder is approximately 5.657 feet.
Therefore, the base of the ladder is approximately 5.657 feet from the house.