Find the range of possible measures of the third side. \[ 8,17 \]

To find the range of possible measures for the third side of a triangle when the lengths of the other two sides are 8 and 17, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, we can set up the inequalities: 1. \( x + 8 > 17 \) leads to \( x > 9 \) 2. \( x + 17 > 8 \) leads to \( x > -9 \) (this is not a restriction since \( x \) must be positive) 3. \( 8 + 17 > x \) leads to \( x < 25 \) Combining these, we find that the measure of the third side \( x \) must satisfy: \[ 9 < x < 25 \] Thus, the range of possible measures of the third side is greater than 9 and less than 25.