Final answer:
The third side of a triangle must be greater than the difference and less than the sum of the other two sides. This is based on the triangle inequality theorem, which is different from calculating the third side length using the Pythagorean theorem for right triangles.
Step-by-step explanation:
The measure of the third side of a triangle, when the lengths of two sides are known, must fall between the sum and the positive difference of those two side lengths. This is derived from the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side, and the difference must be less than the length of the remaining side. For example, if we have two sides measuring 8 units and 5 units, the third side must be greater than 3 units (8 - 5) and less than 13 units (8 + 5).
The Pythagorean Theorem, which states that a² + b² = c² for a right triangle, is a specific case that applies to the lengths of sides when one angle of the triangle is 90 degrees. However, the calculation of the third side using the Pythagorean Theorem is not the same as applying the triangle inequality theorem, which applies to all triangles, not just right-angled ones. Thus, when dealing with non-right triangles, we rely on the triangle inequality theorem to determine the range within which the third side must lie.