The 'height' of the ceiling is eight feet. [=the ceiling is eight feet above the floor; the ceiling is eight feet high]
It was 'the height of' stupidity to quit the team. [=it was extremely stupid to quit the team]
He was 'at the height of' his fame when he died. [=he died when he was most famous]
(..) Then one day, I was walking past a building site. A skyscraper. And I thought, "l could do that." You see, these people down here... a lot of them are afraid of heights, you know what I'm saying? That makes me uniquely qualified. And besides, it feels like a little bit of home up here. (..)1998 City of Angels