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.