The noun height has 4 senses (first 4 from tagged texts)
1. (15) height, tallness -- (the vertical dimension of extension; distance from the base of something to the top)
2. (4) acme, height, elevation, peak, pinnacle, summit, superlative, meridian, tiptop, top -- (the highest level or degree attainable; the highest stage of development; "his landscapes were deemed the acme of beauty"; "the artist's gifts are at their acme"; "at the height of her career"; "the peak of perfection"; "summer was at its peak"; "...catapulted Einstein to the pinnacle of fame"; "the summit of his ambition"; "so many highest superlatives achieved by man"; "at the top of his profession")
3. (3) stature, height -- ((of a standing person) the distance from head to foot)
4. (1) altitude, height -- (elevation especially above sea level or above the earth's surface; "the altitude gave her a headache")