Answer: 29
Work Shown
a = 15
b = 15
c = missing side
b-a < c < b+a ...... modification of the triangle inequality theorem
15-15 < c < 15+15
0 < c < 30
If c is a whole number, then the possible values for c are {1,2,3,..., 27,28,29}. In other words, c is between 1 and 29 inclusive.
The largest possible length for the third side is c = 29
c = 30 isn't possible because it results in a straight line rather than a triangle. This is why "or equal to" isn't involved with the inequality signs.