I know this is isn't exclusive to my country, buuut…
So there are vocational high schools. There are a lot, but just a handful of them belong to a certain university, it's a polytechnic, which is actually in charge of validating the technical degrees.
Cause vocational high schools prepare you for university but they also teach you a technical degree.
Having said this, (and currently suffering my choice of going to one of these, and having to write a mini thesis in about three months), this is my list of what the Riordanverse characters would choose as their technical degree.
Annabeth: Computer Assisted Drawing. This is basically pre Architecture. Either this or construction, but I feel she'd study the former.
Leo: Machines with Automated Systems. This is basically pre mechanical engineering and it's very hands on.
Hazel Levesque: either Computer Assisted Drawing or Metallurgy. She's very artistic hence why Drawing and she could learn to create beautiful jewels, and draw the mechanical plans (you also learn this here), or she's just a natural at metallurgy.
Percy Jackson: I feel like he's the kinda guy that doesn't know what to study and people recommended him to go into a strong math-related field because it'd probably be easier to switch areas and he agrees and then goes into Machines with Automated Systems because it's also a big field, or Mechatronics.
Will Solace: Nursing. It's technical level, but it's still the closest to medicine. I feel like he'd also learn really valuable lessons that he'd appreciate. He'd also have to take etymology :)
Nico: I feel like he'd also go into health sciences, but in clinical laboratory technician. He's interested in human health but not in dealing with patients/people.
Frank Zhang: I feel like he'd also get into clinical laboratory technician, as it's the closest there is to veterinary.
Reyna: Maybe Administration? Or accounting. She's in administrative sciences but definitely nothing related to tourism. She'd also have to take law :)
Jason: Aeronautics. Need I say more?
Piper: Marketing, probably because of her dad. It's also a social science
Thalia: Automotive systems. She was told it was for men, so she got there. Not Aeronautics because her dad's in the field and they have a bad relationship.
Grover: Ecology. It's in the biological and health sciences field.
Anyway, this is my take. Lmk if you think something else.
One last thing, only 3/4 areas are taught in this university. The areas are: physics and maths sciences and engineerings, biological and health related sciences, and social and administrative sciences. The one area that isn't imparted is Humanities and Arts.
Unless I specify, they're all in the engineering field.
