To solve the right triangle, I'll need to understand what each of the variables represents in the triangle you've described. Typically, in a right triangle, we have:

• The two legs (denoted as U and T or other symbols).
• The hypotenuse (usually denoted as S).
• Two angles, one being the right angle (which is 90°), and the other two being acute angles, U and T.

However, you've provided just a few terms:

• TU (the length of a side or hypotenuse),
• m∠U and m∠T (the angle measures).

Could you provide more context or clarify which side lengths are known and what is the right angle? For example, you might want to specify which sides are known or if the angle measures are given.

If you'd like, you can upload a photo of the triangle for further clarification.