1. **State the problem:** We have a right-angled triangle ABC with angle B as the right angle. Given lengths are $AB = 52.5$ cm and $AC = 59.5$ cm. We need to find the length $BC$. 2. **Recall the Pythagorean theorem:** In a right-angled triangle, the square of the hypotenuse ($AC$) equals the sum of the squares of the other two sides ($AB$ and $BC$): $$AC^2 = AB^2 + BC^2$$ 3. **Rearrange to find $BC$:** $$BC = \sqrt{AC^2 - AB^2}$$ 4. **Calculate the squares:** $$AC^2 = 59.5^2 = 3540.25$$ $$AB^2 = 52.5^2 = 2756.25$$ 5. **Subtract to find $BC^2$:** $$BC^2 = 3540.25 - 2756.25 = 784$$ 6. **Find $BC$ by taking the square root:** $$BC = \sqrt{784} = 28$$ **Final answer:** The length of side $BC$ is $28$ cm.