Why do we need Trigonometry?
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Trigonometry is mainly used for measuring distances. For example, the distance between two planets, the height of some mountain, the diameter of some planet or star, depth of an ocean, etc. Anywhere there is the need for measuring distances (including astronomical distances), trigonometry proves useful. But this is not the end. It is useful in several branches of physics like Statics, photometry, mechanics, electromagnetism, etc. It is used every now and then in engineering from the study of vibrations to the study of differential equations, almost everywhere there is some usage of trigonometry.
The uses of trigonometry are so vast that it is truly impossible to note down each of them