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Cosine theorem

Lecture



Theorem

The square of any side of the triangle is equal to the sum of the squares of the other two sides without doubling the product of these sides by the cosine of the angle between them.

  Cosine theorem

Evidence.

Let there be Δ ABC.
Prove that

  Cosine theorem

We have vector equality

  Cosine theorem

Square the left and right sides of the equation, we get

  Cosine theorem

Or

  Cosine theorem

The theorem is proved.
created: 2014-10-05
updated: 2021-03-13
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Planometry

Terms: Planometry