1
  • I know the tower's height — with the
  • I know the Bryan’s height — without the

Questions:

  1. What's the general rule for using the with possessive ('s)?
  2. In the first sentence the is used because of definite tower or definite height?
4

Answering your second question first: In the first sentence, the refers to the tower, not the height.

That's the answer to your first question, too: in your examples, the the has nothing to do with the possessive 's. You could remove "height" and read the sentences this way (with "know" meaning "to be familiar with" instead of "to be aware of a fact"):

  • I know the tower.
  • I know Brian.

People's first names don't require an article in English, but countable nouns like "tower" do, so there you have it. You could also rewrite the sentences as:

  • I know the height of the tower.
  • I know the height of Brian.

"Height" takes the article both times, but "Brian" still doesn't need it.

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