Final answer:
The range for the measure of the third side of the triangle is 12 < third side < 42.
Step-by-step explanation:
To determine the range for the possible values of the measure of the third side of a triangle with two given sides, 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. In this case, the two sides are 15 inches and 27 inches. Therefore, the range for the measure of the third side is:
27 - 15 < third side < 27 + 15
12 < third side < 42
Learn more about triangle inequality theorem