### 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 BC^{2} = BD^{2} + CD^{2}, so

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 |