Note, however, that the Constitution in this diagram isn't all the way to the edge of the frame, nor are Discovery's nacelles completely in frame. IOW, Discovery is roughly twice the length of the Constitution class, including the nacelle tips. That would out it in the 550-600 meter range. (289x2 = 578 meters).
Well, there are three rows of interior windows in the shuttle bay before the viewing gallery near the roof. So that's four decks, and then the "floor" deck of the shuttlebay makes five. So it's a five-deck shuttlebay, which would give us a height of about 12 meters with a 2.5m standard deck height.