Joe built a tree house 12 ft. up in a tree. He wants to build a ladder that will lean up against the tree so that
his house is easily accessible. If the bottom of the
ladder is 9 ft. from the tree, how tall must the ladder
be to rest directly against the house?

To find this, we simply do the pythagorean theorem. A^2+B^2=C^2. We do this because when the ladder is up against the tree, it creates a right triangle. 9ft is the base and the height is 12ft. We need to find C^2 which is the hypotenuse.
12^2+9^2=C^2
144+81=C^2
225=C^2
15=C
The ladder must be 15 feet tall

One unique triangle, because those angles add up to 180, and that's how many degrees there are in one triangle.