The image shows a right-angled triangle $\triangle ABC$, with angle $C$ being 90°. The side lengths provided are:

• $AC = 12 \, \text{cm}$,
• $AB = 15 \, \text{cm}$.

The problem asks for the length of side $BC$.

We can apply the Pythagorean Theorem, which is given by:

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

Substitute the known values:

$15^2 = 12^2 + BC^2$

Now, solve for $BC$:

$225 = 144 + BC^2$ $BC^2 = 225 - 144 = 81$ $BC = \sqrt{81} = 9 \, \text{cm}$

Thus, the length of side $BC$ is $9 \, \text{cm}$.

Would you like further details or have any questions?

Here are five related questions:

1. What is the Pythagorean Theorem and how is it used in right triangles?
2. If side $BC$ was 10 cm, how would the length of $AB$ change?
3. What is the formula for finding the hypotenuse in a right triangle?
4. Can the Pythagorean Theorem be applied to non-right triangles?
5. How do you calculate the area of a right triangle?

Tip: In any right triangle, the Pythagorean Theorem only applies when one angle is exactly 90 degrees.