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?

Answer 1

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.