For a mountain:High (mountain with the highest elevation) For a building:tall (tallest building)

You may have seen or heard A British English way of saying A bridge has a low height. For vehicles to pass under. most often referred to as "headroom". Now over the past 40 years slowly replaced by International signs on all major roads and Motorways. http://www.ukmotorists.com/lowbridge_signs.asp visit this web page and scroll down a little. "low bridge height at Beckwood" the sign is mixing older and modern International systems. you may have chosen the wrong answer too quickly. (Talking about mountain or building). Is it used? answer is yes

The answers so far all avoided answering the question; the opposite of low height is great height.

Sophia, so it's correct to say tall building or tall mountain?

Usually people say "tall." It is a unusual to say "high height" :)