There are 3 primary ways to prove triangles similar:
SSS | AA | SAS
In the problem, you are only given a single side and a single angle. So you pretty much have SA, which is insufficient to prove similarity. You would either need another angle or two more sides (one more side is insufficient as you would need an included angle).
You could just think about this one too. Segment TS can be made arbitrarily long or short (as long as it's between 0 and 12) and segment US can be adjusted to keep the hypotenuse at length 12. This can all happen while angle S remains a right angle.