Find out whether a triangle with sides 9 cm, 5 cm, 6 cm is acute-angled, rectangular or obtuse-angled.

Let us denote the larger side of the triangle by a, and the smaller sides by b and c.

To determine the type of triangle, we need the sum of the squares of the smaller sides (b ^ 2 + c ^ 2) and the square of the larger side.

If a ^ 2 = (b ^ 2 + c ^ 2), then the triangle is right-angled.

If a ^ 2> (b ^ 2 + c ^ 2), then the triangle is obtuse.

If a ^ 2 <(b ^ 2 + c ^ 2), then the triangle is acute-angled.

a ^ 2 = 81.

(b ^ 2 + c ^ 2) = 36 + 25 = 61.

81> 61, therefore, the triangle is obtuse.

Answer: The triangle is obtuse.