An 18 foot ladder is leaned against a wall. If the base of the ladder is 7 feet from the wall how high up on the wall does the ladder reach

The ladder makes a rectangle triangle with the floor and wall, the ladder is the hypothenuse. So we use Pythagoras theorem: the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides

So we have:

hyp^2 = wall^2 + floor^2

and plugging data in:

18^2 = wall^2 + 7^2

324 = wall^2 + 49

wall^2 = 275

wall = 16.58