Trigonometry. Take a reference point like sea level. Measure triangle angles very accurately and use math to calculate the distances. Surveyors would use rods and chains to measure known distances across ground to set baselines. Then you measure angles from those reference points to get the numbers.
Today, the measurements are largely electronic with total stations taking the distance and angle measurements with lasers. Also GPS measurements can be done with survey beacons providing a fixed reference point to compensate for GPS inaccuracy.
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