1. **Problem:** Determine if a triangle with sides 8 cm, 15 cm, and 17 cm is right-angled. 2. **Formula:** Use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse ($c$) equals the sum of the squares of the other two sides ($a$ and $b$): $$c^2 = a^2 + b^2$$ 3. **Check:** Identify the longest side as the hypotenuse candidate: 17 cm. Calculate: $$17^2 = 289$$ $$8^2 + 15^2 = 64 + 225 = 289$$ 4. Since both sides satisfy the Pythagorean theorem ($289 = 289$), the triangle with sides 8 cm, 15 cm, and 17 cm is a right-angled triangle. **Final answer:** Yes, the triangle is right-angled.