You just have to apply the reciprocal of the pythagoras theorem.
Let's do it then !
8 in, 15 in and 17 in
The longest length here 17 inches right ?
You have to verify if : 8² + 15 ² = 17²
8² = 64
15² = 225
Therefore 8² +15² = 64 + 225 = 289.
Now : 17² = 289.
So, 8in, 15in and 17in will go in the box "right triangle".
And in that case, you have already guessed, 4in, 15in, 17in would go the box "Not a Right Triangle".
Hope this helps !
Photon