Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. In this video we look at the use of trigonometry with right triangles, solving for both sides and angles.

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BTW for those interested - the history of trigonometry history is fascinating!
The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
The use of trigonometry really took off due to it's use in navigation - trigonometry has been used for locating latitudes and longitudes of sailing vessels, plotting courses, and calculating distances during navigation.
Trigonometry is still used in navigation through such means as the Global Positioning System and artificial intelligence for autonomous vehicles.

But the truly cool trigonomic endevour was The Great Trigonomical Survey.
The Great Trigonometrical Survey was a project which aimed to measure the entire Indian subcontinent with scientific precision. It was begun in 1802 and completed of it in 1871.
Among the many accomplishments of the survey was measurement of the height of the Himalayan giants: Everest, K2, and Kanchenjunga. The Survey had an enormous scientific impact as well, being responsible for one of the first accurate measurements of a section of an arc of longitude.
Triangulation surveys were based on a few carefully measured baselines and a series of angles. The initial baseline was measured with great care, since the accuracy of the subsequent survey was critically dependent upon it. Various corrections were applied, principally temperature. An especially accurate folding chain was used, laid on horizontal tables, all shaded from the sun and with a constant tension. The early surveys made use of large and bulky theodolites made by William Carey, a Zenith sector made by Jesse Ramsden and 100-foot (30 m) chains!
Interesting aside - Everest was one of the leaders of the survey - and his name was pronounced Eve-rest not Ever-est! To donate to the tecmath channel: https://paypal.me/tecmath?locale.x=en_AU To donate to the tecmath channel: https://paypal.me/tecmath?locale.x=en_AU
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