This is the 2610th most frequent Japanese word.
手渡さ
"To hand over" or "to pass."
In this sentence, '手渡さ' (tewatasana) is the verb root form for 'hand over', indicating an action of directly giving something to someone.
彼は手紙を友人に手渡さなければならない。
He must hand the letter to his friend.
Here, '手渡さ' is part of the passive form '手渡される' (tewatasareru), showing the state of being handed something.
手渡される喜びを感じる。
Feel the joy of being handed over something.
In this usage, '手渡され' is the base of the formal passive past '手渡されました', denoting a respectful action performed by the teacher.