A 12​-foot ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 11 feet from the base of the building. How high up the wall does the ladder​ reach?

Answer 1

Let x represent the height up the wall that the ladder reaches.

Using the Pythagorean theorem, we can find the height up the wall:

(11)^2 + x^2 = (12)^2
121 + x^2 = 144
x^2 = 144 - 121
x^2 = 23
x = √23

Therefore, the ladder reaches a height of approximately 4.8 feet up the wall.