A wall is supported by a brace 10 feet long. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach?
Think of the right triangle frmed by the wall, the floor and the brace, and use the Pythagorean theorem. The brace is the hypotenuse.
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You're welcome! I'm glad I could help you.
To find out how many feet up the wall the brace reaches, 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 lengths of the other two sides.
In this case, the brace is the hypotenuse of the right triangle, and we know the length of one side (the base of the triangle) is 6 feet, and the length of the other side (the height of the triangle) is what we need to find.
Let's call the height of the triangle "h". According to the Pythagorean theorem, we have:
(10 feet)^2 = (6 feet)^2 + h^2
Simplifying the equation:
100 feet^2 = 36 feet^2 + h^2
Subtracting 36 feet^2 from both sides of the equation:
64 feet^2 = h^2
Taking the square root of both sides:
8 feet = h
Therefore, the brace reaches 8 feet up the wall.
I hope this explanation helps! Let me know if you have any further questions.