I was happy to see the policeman who saved my cat.
even if we don't know the policeman's name, it's still a particular policeman because it is the one who saved the cat.
Whereas i found a sentence which contains adjective clause but didn't use the:
A woman who fell 10 meters from High Peak was lifted to safety by a helicopter.
My first question: why doesn't above sentence use the even though it is using an adjective clause?
My second question: in the sentence below,
The books that have red covers are new.
Do we use the because of mentioning that have red covers or because we are talking about some specific books, for example the books on the table?
I mean do you agree with the order below for the last sentence?
First we have The books, so we are talking about some specific books (e.g. on the table) ,Then we restrict those books to the ones that have red covers and at last we add some more information about them(are new).