The lengths of two sides of a right triangle are 5 inches and 8 inches. what is the difference between the two possible lengths of the third side of the triangle? round your answer to the nearest tenth.

Let x be the third side. The two cases that allow us to determine the length of the third side are: (1) let x be the hypotenuse and (2) let 8 be the hypotenuse and solve for x. Through the Pythagorean theorem,
 
Case 1.           x² = 8² + 5²       ; x = 9.4
Case 2.           8² = x² + 5²       ; x = 6.2

Thus, the difference is approximately 3.2.