To determine a missing angle using the cosine rule, you need to rearrange the formula to isolate the angle.

The cosine rule is expressed as:

In this equation, $a$, $b$, and $c$ represent the lengths of the sides of a triangle, while $C$ is the angle opposite side $c$. To find the angle $C$, we will rearrange the formula to solve for $\cos(C)$.

First, isolate $\cos(C)$ by rearranging the equation:

Next, substitute the known values of the sides $a$, $b$, and $c$ into this equation. For instance, if you have the lengths of all three sides of the triangle, you would plug these values into the formula like this:

After calculating the value of $\cos(C)$, use the inverse cosine function, often denoted as $\cos^{-1}$ or arccos, on your calculator to find the angle $C$:

Ensure that your calculator is set to the appropriate mode (either degrees or radians) based on the context of your problem. This method provides an accurate way to determine the measure of the missing angle.