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how can trigonometry use in metallurgy
Depending on your career, you may or may not need trigonometry. If your job does not require a lot of math, it is unlikely that you will use trigonometry very often, however, this is not a reason not to study it. The skills and discipline developed in your trigoometry class will help you no matter what career you choose.
One example of an astronomer's use of trigonometry is determining the distance to a star by triangulation.
Mechanics use trigonometry to find angles mostly used in body or chassis work.
The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus