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Measurements of a trigon (or triangle).
Through the usage of trigonometry and a protractor.
The purpose of trigonometry is to gather as much accurate measurements of distances given little information about angles or other distances. It is used in engineering, astronomy, city planning, drafting and designing, and construction.
Using trigonometry and Pythagoras' theorem.
Because it is a branch of mathematics that is concerned with measurements of angles and sides of triangles, and following from that, areas and other characteristics.