Final answer:
For side lengths 9 and 8, the range would be 1 < third side < 17.
Step-by-step explanation:
To find the range of possible measures for the third side of a triangle given two side lengths, we can use the triangle inequality theorem.
According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, for a triangle with side lengths 9 and 8, the range of possible measures for the third side would be any value greater than 1 but less than the sum of the two known side lengths:
1 < third side < (9 + 8)
=> 1 < third side < 17.