Find the ratio of the lengths of chord AB to arc AB

Question

The chord AB of a circle subtends an angle of 60 degrees at the centre. Find the ratio of the lengths of chord AB to arc AB.

I tried $sin60 = AB/r = √3/2$

Therefore $r = 2$ and $chordAB = √3$

Therefore $arcAB = rθ = 2 * 60 = 180$

and so the ratio is $√3/180$

This just doesn't seem right and is definitely not the right answer. Any hints? Thanks

Answer 1

It's $$\frac{R}{\frac{2\pi R}{6}}=\frac{3}{\pi}.$$