"Those castles are big."
Translation:Ty hrady jsou velké.
Ty is used with masculine INanimate and feminine nouns. Masculine animate nouns use ti. You can see the full declension table for demonstrative pronouns (and a lot of other very useful things) here: https://en.wikipedia.org/wiki/Czech_declension#Demonstrative_pronouns.
You could use "velký" it's informal and grammatically incorrect but common in speaked language.
Velkí is totally wrong, "velcí" is the correct word. And you use this only with plurar and "životné" masculine words. Because masculine nouns split into "životné" and "neživotné". Usually (but not always) living things are "životné". E.g.: muž (a man) is "životné", therefore velcí muži (big men).