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Triangles and TrigonometryIntroduction

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By the early 19th century, explorers had discovered most of the world. Trade and transportation was booming between distant countries, and this created a need for accurate maps of the entire planet.

Today we have satellites that can take photos from above – but 200 years ago, creating maps was a difficult and time consuming task. It was done by mathematicians like Radhanath Sikdar, who worked on the Great Trigonometrical Survey: a century-long project to measure all of India, including the Himalayan mountain range.

The theodolite, a surveying instrument

Of particular interest was the quest to find the highest mountain on Earth. There were a few different candidates, but from hundreds of kilometers away, it was difficult to tell which one was the highest.

So how do you measure the height of a mountain?

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Today we can use satellites to measure the height of mountains to within a few centimeters – but these did not exist when Radhanath was surveying India.

Climbers use altimeters to determine their altitude. These devices use the difference in air pressure at different heights. However this would have required someone to actually climb to the top of every mountain – an extremely difficult feat that was not achieved until a century later.

You could also try using similar triangles, like we did in the previous course. This method requires knowing the distance to the base of the mountain: the point at sea level that directly below its summit. We can do this for trees or tall buildings, but for mountains this point is hidden underneath hundreds of meters of rock.

Edmund Hillary and Tenzing Norgay were the first to reach the top of Mount Everest, in 1953.

But there are more advanced geometric techniques, which Radhanath used to discover the highest mountain on Earth: it is now called Mount Everest. His measurement is only a few meters off today’s official height of 8848 meters.

In this course you will learn about many different features and properties of triangles. These will allow you to measure the height of mountains, but they are also of fundamental importance in many other areas of mathematics, science and engineering.