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Al-Kashi's theorem

The theorem of Al-Kashi can be used to calculate angles and sides of a triangle



We calculate the formula with figure 17.

In the right-angled triangle ACD applies

The sides of the right-angled triangle BCD are determined by BC2 = BD2 + CD2, so

This is the cosine rule and applies to any triangle. If ∠α = 90° then cos α = 0 and you have the Pythagorean theorem



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

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