Let x denote PR, then RQ = 50-x. Using the tangens function you can set up 2 equations:

..... and .....

Set equal the RHS of the two equations and solve for x, afterwards you can use one of the two equations to get the length of RS. I've got

I've modified your sketch a little bit. (see attachment)Find TU.

According to the drawing you can set up 2 equations:

..... and .....

Solve the second equation for y, plug in this term into the first equation and solve for x.

I've got