A 13-foot ladder is leaning against a 12-foot-tall vertical wall. Use a Pythagorean triple to find out how far the bottom of the ladder is from the wall.
To find out how far the bottom of the ladder is from the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder forms the hypotenuse of the right triangle, and the wall represents one of the legs. Let's call the distance between the bottom of the ladder and the wall "x" (the other leg of the triangle).
According to the problem, the ladder is 13 feet long, and the wall is 12 feet tall.
Using the Pythagorean theorem, we have:
x^2 + 12^2 = 13^2
Simplifying, we get:
x^2 + 144 = 169
Subtracting 144 from both sides, we have:
x^2 = 25
Taking the square root of both sides to solve for x, we get:
x = 5
Therefore, the bottom of the ladder is 5 feet from the wall.