Final answer:
To classify a triangle as acute, obtuse, or right, we can use the Pythagorean theorem. For the triangle with sides 8 cm, 15 cm, and 16 cm, the sum of the squares of the two shorter sides is greater than the square of the longest side, confirming it is an acute triangle.
Step-by-step explanation:
To classify a triangle with side lengths of 8 cm, 15 cm, and 16 cm as acute, obtuse, or right, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
If the triangle is not a right triangle, we can determine if it is obtuse or acute by comparing the square of the longest side with the sum of the squares of the other two sides:
If c² > a² + b², then the triangle is obtuse.
If c² < a² + b², then the triangle is acute.
For our triangle, the longest side is 16 cm. Therefore, c = 16, a = 8, and b = 15. Calculating:
16² = 256
8² + 15² = 64 + 225 = 289
Since 256 < 289, this confirms that our triangle is acute. Hence, the triangle with side lengths of 8 cm, 15 cm, and 16 cm is an acute triangle as the sum of the squares of the two shorter sides is greater than the square of the longest side.