The Law of Cosines is super helpful for finding unknown angles in a triangle, especially when you know the lengths of the sides. It works great for triangles that do not have a right angle. Here's what the formula looks like:

$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$

In this formula:

• $c$ is the side across from angle $C$.
• $a$ and $b$ are the other two sides of the triangle.

Let’s break down how to use it to find an angle:

1. Identify the Sides: Start by knowing the lengths of two sides and the third side. Let’s call these sides $a$, $b$, and $c$.

2. Plug In the Values: Rearrange the formula to solve for $\cos(C)$: $\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$

3. Calculate the Angle: After you find $\cos(C)$, you can figure out angle $C$ by using the arccosine (which is the inverse cosine) of that value: $C = \arccos\left(\frac{a^2 + b^2 - c^2}{2ab}\right)$

It’s quite simple! Once you understand it, you’ll feel like a geometry superstar!