A 10-foot-tall ladder rests against an 8-foot wall. The wall and ground form a 90-degree angle.
How many feet away from the wall is the bottom of the ladder?
The distance from the wall to the bottom of the ladder can be found using the Pythagorean theorem. In a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the height of the wall and the distance from the wall to the bottom of the ladder).
Applying this to the given information, the length of the ladder (hypotenuse) is 10 feet, and the height of the wall (one of the other sides) is 8 feet. Let's represent the distance from the wall to the bottom of the ladder as x.
According to the Pythagorean theorem:
x^2 + 8^2 = 10^2
x^2 + 64 = 100
Subtracting 64 from both sides:
x^2 = 36
Taking the square root of both sides:
x = 6
Therefore, the bottom of the ladder is 6 feet away from the wall.