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Cosine rule

In each triangle you can apply the cosine rule to calculate angles and sides



We calculate the formula here with figure 17.

In the right triangle ACD holds

The sides of triangle BCD are determined by BC2 = BD2 + CD2, so

The cosine rule is valid for all triangles. If ∠α = 90° then cos α = 0 and you have the Pythagorean theorem.



The Persian mathematician Al-Kashi (believed to be 1380 - 1429) was the first to provide an explicit statement of the law of cosines in a form suitable for triangulation.

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