A 21-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 20 feet from the base of the building. How high up the wall does the ladder reach?
We can solve this problem using the Pythagorean theorem. Let's assume that the height the ladder reaches on the wall is represented by the variable $h$. The base of the ladder on level ground is given as 20 feet. Thus, we have a right triangle with a base of 20 feet, a height of $h$ feet, and a hypotenuse of 21 feet.
Using the Pythagorean theorem, we can write:
$20^2 + h^2 = 21^2$
Simplifying, we get:
$400 + h^2 = 441$
Subtracting 400 from both sides, we have:
$h^2 = 41$
Taking the square root of both sides, we find:
$h = \sqrt{41}$
Therefore, the ladder reaches approximately $\sqrt{41}$ feet up the wall.