A formula known as law of cosine (sometimes also referred to as Carnot's rule) states that, in any triangle ABC, you have
![\overline{AB}^2 = \overline{BC}^2+\overline{AC}^2-2\overline{AC}\overline{BC}\cos(\alpha)](https://img.qammunity.org/2020/formulas/mathematics/high-school/1kchf4yi4b2p9mqg1u73iau7bsbd5zetls.png)
where
is the angle between AC and BC. This formula generalizes Pythagoras' theorem, since it doesn't require the triangle to be right. In your case, we have
![[tex]AB = \sqrt{(1)/(4)+(1)/(9)-2\cdot(1)/(2)\cdot(1)/(3)\cdot\cos(100)} = \sqrt{(13)/(36)-(\cos(100))/(3)} \approx 0.65](https://img.qammunity.org/2020/formulas/mathematics/high-school/ba8n8lvi7w5h149z5k0mioa7kmapkw5fdb.png)