First of all, if you can ask any question, you only need one, "If I were to ask you for one person who is a liar, and if you were to lie or tell the truth based on how you are going to answer this question, then who could you not pick?" No matter who you ask, the answer must always be a truth-teller.
However, if I understand correctly your question, you can only ask person A, "Is person B a truth-teller or a liar?"
To find the minimum number of questions needed, you can assume the best circumstances. So let's pick a person B. Let's assume that B is a truth-teller.
Now you go ask 27 people (who all happen to be truth-tellers) if B is a truth-teller. They all say yes. Either B is a truth-teller or a liar. If B is a liar, then the 27 people who said that B was a truth-teller lied. If both B and the 27 people who lied are liars, then there are 28 liars. Since there are 27 liars (69-42), B must be a truth-teller.
Therefore, if the first person you pick happens to be a truth-teller, and everyone you ask tells the truth (not necessarily being truth-tellers), then you can figure out for sure that B is a truth-teller in 27 questions.
Now, I haven't proven that 27 is the minimum number of questions that can be asked to determine a truth-teller (nor do I know how), but I did prove that you can do it in only 27 questions. There may very well be a faster way to determine a truth-teller.
I have thought about how to prove what the absolute minimum number of questions needed to determine a truth-teller is, and I have decided it is impossible. The goal is to prove that someone is a truth-teller. But how can you know the minimum number of questions required to prove that unless you know every possible way to prove that someone is a truth-teller. I can come of with a list of several ways to do so, but how can I know that there isn't another way? You may also try to go through every possible number of moves up to 27 and try to prove that you can't determine a truth-teller with that number of moves, but even then you need to know every possible way to prove that someone is a truth-teller in order to prove that you can't do it with that number of moves. I could be wrong, but I think that if my assumption that you can't know 100% whether you know all the ways to prove that someone is a truth-teller, then you can't know 100% whether a certain number of questions is the minimum number possible.