Iwill give brainliest to whoever is correct.

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