A10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 9 feet from the base of the building. how high up does the ladder reach?

First draw a picture like the one I have (see attached).

You should know the Pythagorean theorem, which is
, where a and b are the legs of the triangle and c is the hypotenuse (remember the hypotenuse is the longest side of the triangle and is opposite of the right angle).

In this case, 
a = 9
b = x
c = 10

Or you could have switched up a and b and had a = x and b = 9 because they are both legs of the triangle.

Using the formula,
.
Note that we elimante the negative root 19 because sides of a triangle must be positive.

The ladder reaches a height of , or approximately 4.359 ft.