Will the following sides 14 feet ,17 feet, 30 feet make a right triangle, if so explain why?

Well I don't know !
Let's work it out.

IF the triangle IS a right triangle, then

         (the shortest side)² + (the medium side)² = (the longest side)²

Let's test this one:

         (14)²  =  196
         (17)²  =  289

         (the shortest side)² + (the medium side)² =  (196 + 289) = 485

         (The longest side)² = (30)² = 900 .

         900 is not the same number as 485,
         so these three sides do not make a right triangle.