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Q: Do architects use trigonometry

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They use it to measure angles and lengths

to figure out stuff,they take a measuring cup and measure stuff

Trigonometry is used in many situations and jobs in life, including architects, surveyors, astronauts, physicists, engineers and even crime scene investigators. The latter use trigonometry for example to calculate a projectile's trajectory, to estimate what might have caused a collision in a car accident or how did an object fall down from somewhere (for example from a rooftop).

how can trigonometry use in metallurgy

One example of an astronomer's use of trigonometry is determining the distance to a star by triangulation.

architects use coordinate planes to graph where they want the rooms to be

Well, if Edward Cullen the bloodsucking vampire can use trigonometry. Then I am asuming farmers can as well.

Mechanics use trigonometry to find angles mostly used in body or chassis work.

architects use triangles in their designs because it makes it look cool

Architects often use computers in order to designs homes and other buildings. Architects need to have the ability to draw in order to draft designs.

The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus

Yes

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