If a ladder which is 15 feet long is leaned against a house so that the bottom of the ladder is 5 feet from the house, how high up the house will the ladder reach?

This would form a right triangle with 15 being the hypotenuse, 5 being the base, and the unknown value being the height.
Use Pythagorean theorem to find the missing length.
a^2 + 5^2 = 15^2
a^2 + 25 = 225
Subtract 25 from both sides
a^2 = 200
Take the square root of each side
a = √200
a = 10√2  EXACT answer
a = 14.14 decimal approximation