Question

A 16​-foot ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 5 feet from the base of the building. How high up the wall does the ladder​ reach?

Answer 1

Let the height be h. By the Pythagorean theorem,
h^2 + 5^2 = 16^2
h^2 = 256 − 25 = 231
h = sqrt(231) ≈ 15.20 feet.

So the ladder reaches sqrt(231) ≈ 15.2 ft up the wall.