Is $\cos(11^\circ)$ constructible?

Question

I'm trying to prove whether $\cos(11^\circ)\over \sqrt{1+\sin(15^\circ)}$ is constructible. I suspect it is not, and would like to use the triple angle identity to use RRT and prove there is no constructible root, but to do this I'd need $\cos(33^\circ)$, of which I don't know the exact value. Is there a better way to go about this?

Answer 1

Famously the angle of 20 degrees is not constructible. Since $20=10\times 2$ and $2=90-8\times 11$, this means that angle of 11 degrees is also not constructible.