**Deriving Law of Sines and Law of Cosines**

Our friend, the Pythagorean Theorem, comes to our aid when solving for sides and/or angles in a right triangle. We have now seen that there are formulas (the Law of Sines and the Law of Cosines) that will help us find sides and/or angles when we are not working in a right triangle.

But where did these formulas come from?

Let’s see how these formulas were derived:

**Law of Sines**

Triangle ABC at the right does not contain a right angle. A perpendicular is dropped from vertex B. It can now be observed that:

**Law of Cosines**

Triangle ABC at the right does not contain a right angle. A perpendicular is dropped from vertex B. It can now be observed that: