Al-Kashi's theorem
The theorem of Al-Kashi can be used to calculate angles and sides of a triangle
Explanation
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
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This is the cosine rule and applies to any triangle. If ∠α = 90° then cos α = 0 and you have the Pythagorean theorem
HistoryThe 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. |