Triangulation. Theodolites work in the vertical as well as the horizontal. Nowadays you can use GPS to augment traditional surveying methods. Most national mapping organisations have a datum level against which altitudes are measured. Britain’s is the port of Newlyn, Cornwall and is based on the average of sea level measurements over a six year period about a hundred years ago.
https://www.ordnancesurvey.co.uk/newsroom/news/100-years-of-ordnance-datum-newlyn
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