Final answer:
The length of the third side AB in a triangle with sides of 80.0 m and 105 m must be greater than 25 m and less than 185 m, according to the triangle inequality theorem.
Step-by-step explanation:
To determine the possible lengths of the third side AB in a triangle, we must consider the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Given two sides of a triangle with lengths 80.0 m and 105 m, the length of the third side must be greater than the difference of these two lengths and less than their sum. Therefore, the length of side AB must be greater than 25 m (105 - 80) and less than 185 m (105 + 80).
The length of side AB must be greater than 25 m and less than 185 m. This provides a range from greatest to least possible lengths for the third side of the triangle.
This conclusion is based on the properties of triangles and the application of the triangle inequality theorem. When constructing or analyzing any triangle, it is important to ensure that the third side fits within these constraints for the figure to be a valid triangle.