A 13-foot-long ladder leans against the side of a building. The bottom of the ladder is 5 feet from the base of the building. What height does the ladder reach?

Answer 1

5^2 + h^2 = 13^2
h^2 = 169 - 25 = 144
h = 12 remarkably

Answer 2

You can save yourself some calculation by learning a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples.