Cosine Law

To use the sine laws introduced last section, we need to know at least one complete side length to angle ratio including another known side length or angle. Sometimes we may not have that information, but instead you’re given all three side lengths and no angle. In this case, we can still solve such a triangle using the cosine law. The formulas you’ll need are shown below:


We use these formula under these conditions:

  • Side – Angle – Side (AAS)
  • Side – Side – Side (SSS)
  • Sometimes to solve a triangle, you may have to use both the cosine law and sine law.

Let’s look at a few examples where the cosine law is used to solve triangles.

The purpose of learning these laws is to apply it to real-life. The two videos below will show two separate application problems pertaining to the cosine law.