At 8,849 meters (29,032 feet), Mount Everest is the tallest mountain in the world – but how did we figure that out? In fact, how do we know how high any mountain is? They certainly don’t make measuring tapes that long (plus someone would have to be at the top to read it), so how do people actually go about measuring the height of a mountain?

You know when you sat in that math lesson and thought “pffft, I’ll never use trigonometry in real life”? Well, you’d better dust off your protractor because the most traditional way of measuring a mountain’s height most definitely does involve some trig skills.

It’s a method called triangulation, which requires knowing the distance between two points on the ground, and the angle between both of those points and the peak of the mountain. 

The height of mountains, however, is measured from sea level – which, theoretically, should be the same across the planet – so figuring it out also requires the person doing the measuring to know the elevation above sea level of the point they’re measuring from, as well as taking into account the curvature of the Earth.

When it comes to measuring the angles, things need to be a little more exact than holding up a plastic protractor; that’s where a theodolite comes in, a telescope-looking type of optical precision instrument that can measure both horizontal and vertical angles.

With two angles and the length of one side of the “triangle”, you can then bung all those numbers into a few trigonometric formulas (the sine rule and Heron’s formula can help) and shazam, you’ve got the height of the mountain.

However, this historically used method isn’t necessarily the most accurate. When British army officer Sir Andrew Scott Waugh and his team were measuring Mount Everest as part of the Great Trigonometric Survey, for example, Earth’s atmosphere interfered.

Light can bend in the atmosphere, known as atmospheric refraction, due to changes in the density of the air. This can become more pronounced over longer distances, and because it then makes objects appear taller or shorter than they truly are, measurements made can end up being inaccurate.

Nowadays, it can be simpler and far more accurate to measure a mountain’s elevation by making use of GPS. That’s a good thing when it comes to Mount Everest, because its height can actually change – not because of changes in measuring methods, but because geological events like earthquakes.