I'm testing to see if the sides make up a right triangle (a^2 + b^2 = c^2), but how do I make it so that, no matter the order put in, "c" will always be the largest of the three?

If c is not the largest, simply swap it with another element. The following should be sufficient:

// input values a, b, c here

    if (a > c) {
        // a is bigger, so use it for c
        swap(a, c);
    }
    if (b > c) {
        // either way (note: not "else if"), if b is now bigger, use it for c
        swap(b, c);
    }

    // continue with test for right-triangle

I'll leave it to you to write a function called swap() which swaps it's two arguments (in such a way that the values get returned to the main program!), or just replace the function calls with the code to perform the swap.