The image shows a right-angled triangle ABC, with the right angle at C. What is the formula relating the lengths of its sides?

Step 1: Identify the formula.
The image shows a right-angled triangle $\triangle ABC$, with the right angle at $C$. For a right-angled triangle, the relationship between the lengths of its sides is given by the Pythagorean theorem. Your notes correctly state this rule as:

$$AB^2 = BC^2 + AC^2$$

Here, $AB$ is the hypotenuse (the side opposite the right angle), and $BC$ and $AC$ are the legs (the sides adjacent to the right angle).