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> Yesterday I've noticed some relationships with cosine and square root. Anything interesting about it?
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I was trying to find the smallest width on an hexagon with radius $1.0$ and I noticed that I could get it both by $\sqrt 3$ and the or two times the cosine of $30^\circ$.

[![enter image description here](https://i.stack.imgur.com/sGhjH.png)](https://i.stack.imgur.com/sGhjH.png)

I wondered if there would be more matches and so I notice these even though might look silly...

$2 \times \cos 90^\circ = \sqrt 0$

$2 \times \cos 60^\circ = \sqrt 1$

$2 \times \cos 45^\circ = \sqrt 2$

$2 \times \cos 30^\circ = \sqrt 3$

$2 \times \cos 0^\circ = \sqrt 4$

Is there anything interesting to know about these?

Thanks