A triangle has sides of length 9 cm, 12 cm and 16 cm. Which description of it is correct?

The sides do satisfy the triangle inequality, since 9 + 12 = 21 > 16, so the triangle exists. Now compare the square of the longest side with the sum of the squares of the other two: $9^2+12^2=81+144=225$, while $16^2=256$. As 225 < 256, the angle opposite the 16 cm side is bigger than 90°, so the triangle is obtuse-angled. Equality would have made it right-angled, and 225 > 256 would have made it acute-angled.