15, 30, 35

Try the Pythagorean theorem:

  a² + b² = c²
15² + 30² = 35²
225 + 900 = 1225
     1125 = 1225

That's false, so 15, 30, 35 cannot be used to create a right triangle,
because the Pythagorean theorem does not give equality.

-----------------------------------------

15, 36, 39

Try the Pythagorean theorem:

   a² + b² = c²
 15² + 36² = 39²
225 + 1296 = 1521
      1521 = 1521

That's true, so 15, 36, 39 can be used to create a right triangle,
because the Pythagorean theorem gives equality.

---------------------------------------------------

15, 20, 29

Try the Pythagorean theorem:

  a² + b² = c²
15² + 20² = 29²
225 + 400 = 841
      625 = 841

That's false, so 15, 20, 29 cannot be used to create a right triangle,
because the Pythagorean theorem does not give equality.

--------------------------------------------------------

5, 15, 30

No use to try the Pythagorean theorem on this because, to even have any
triangle at all,  the sum of the two shorter sides MUST be GREATER THAN the
longest side, and 5+15 is only 20, which is not greater than what would
have to be the longest side, namely 30.

-------------------------------------------------------

Answer: 15, 20, 29

Edwin

 as 

Notice also that if 15, 36, and 39 are divided by 3, we get: 5, 12, and 13.

This is actually one of the pythagorean triples:  

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