Let x be the length of the 3rd side.

From triangle inequality, we know:

8 + 15 > x

x < 23

and

8 + x > 15

x > 7

combine the 2 results, we get:

7 < x < 23.

The question now becomes:

Find the number of positive integers that satisfies 7 < x < 23.

We can count the answer, which is 15.

Therefore there are **15** possible lengths for the 3rd side, if it is a +ve int.