영어 관사 문제 세 가지 질문드려요

관사 문제 세 가지 답과 설명 부탁드려요.
1. this is one of the most dangerous substance known to (the man/man)
2. he was lying on the sofa, (the book/book) in hand
3. towards (the/x) end of (the/x) 1950s he visited the Philippines