If a 10-foot ladder leans against a wall and hits the wall at 8 feet, how far is it from the wall at the base?

To determine how far the base of the ladder is from the wall, we can use the Pythagorean theorem. This theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the lengths of the other two sides.

In this scenario, the ladder is the hypotenuse, with a length of 10 feet. The height at which the ladder touches the wall (the vertical side of the triangle) is 8 feet. We need to find the length of the horizontal side (the distance from the wall to the base of the ladder), which we can denote as 'x'.

According to the Pythagorean theorem:

[ a^2 + b^2 = c^2 ]

Here, 'a' is the height (8 feet), 'b' is the distance from the wall (x), and 'c' is the length of the ladder (10 feet). Plugging in the values:

[ 8^2 + x^2 = 10^2 ]

This simplifies to:

[ 64 + x^2 = 100 ]

By rearranging the equation to solve for