Do they just kind of compare it to other mountains and give an estimate? Or is there an actual way to accurately measure its height?
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Well now we can use GPS satellites and other satellite mapping tools like synthetic aperture radar, but before that, we used a lot of trigonometry. To measure the height of a mountain, surveyors used a method called triangulation. Observers examined the peak from several points. Knowing the distance from the points to the mountain, they were able to measure the angle from the summit to their observation points. Given the distance and the angle, they used trigonometry to calculate the mountain’s height relative to themselves. To calculate the mountain’s actual height above sea level, the observers themselves had to know their own elevation above sea level. They also had to take into account things like atmospheric refraction which can make distant objects appear higher or lower as light bends through the atmosphere. This method is remarkably accurate. In 1856, surveyors measured the peak of Mt. Everest to be 29,002 ft (8,840 m) above sea level from over 100 miles away. They were only off by 27 ft (8 m).
They start at sea level being zero and measure up. Also, i believe they use pressure to measure the height accurately. The higher you are up the mountain the less atmospheric pressure there is and they can convert the pressure difference to height. This is possible because atmospheric pressure is the amount of air above you pushing down causing the pressure. And the higher you go there is less air above you causing a lower pressure.
Edit: This was my best guess at 3am. Just went sky diving and you wear what looks like a watch but actually measure your height with pressure.
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