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Cosine angle

Lecture



The cosine of the acute angle of a right triangle is the ratio of the adjacent leg to the hypotenuse.

  Cosine angle

The cosine of the angle α is denoted by: cos α.

  Cosine angle

Theorem

The cosine of the angle depends only on the degree measure of the angle and does not depend on the location and size of the triangle.

  Cosine angle

Evidence.

Let Δ ABC and Δ A2B2C2 be given - right triangles. ∠ A = ∠ A2 = ∠ α. It is required to prove that

  Cosine angle

Construct Δ AB1C1 equal to A2B2C2. Straight lines B1C1 and BC are perpendicular to AC and therefore parallel to each other. Then, by the proportional segments theorem

  Cosine angle

A pop building A2C2 = AC1 and A2B2 = AB1, then

  Cosine angle

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

Terms: Planometry