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]
(..) - It's warmer. - No, that's all right. I'm fine. You're not. You're freezing. I don't like high places. You can't fight. You can't see. You're afraid of heights and almost everything else probably. What are you doing here, Sam? On the morning of my th nameday, my father came to me. (..)2011 TvShow: Game of Thrones Title: Cripples, Bastards, and Broken Things Season: 1 Episode 4