What is your rod and reel setup? Using the lightest tackle possible probably isnt the best idea for sharks over 3ft... not sure how many yards of that 30lb braid you have but you'll need a lot to handle a decent size shark. A sizeable shark will spool out 100+ yards of line on the first run alone. Even if you max out your drag at rougly 50% of line weight (so ~15lbs) there is a good chance youll get spooled. A reel with a really good drag system and enough capacity to hold lots of heavy test line is pretty essential to land these fish safely.

Theoretically its possible to catch a big shark on light tackle like yours but youll need an insane amount of line and the fight would probably take hours. Not an ideal situation for you or the shark, and it would only take one good head thrash to pop your line and leave a shark swimming around with 300yds of your 30lb braid trailing behind. Down in the gulf when we fish for sharks from shore its almost always involves fairly long, heavy-duty leaders that can stand up to a sizeable shark thrashing about... think 1000lb or 500lb mono leader instead of your 20lb. Steel wire leaders for the hook to prevent cuts against the teeth. And typically large 3x thick 12/0 or larger inline circle hooks.

Lunch break is ending but I'll link some good shark fishing recources later this afternoon if you want to get a better idea of what you'll need to target the big boys.