How to calculate how long each side of an regular polygon should be to fit on a grid of x*x size?

Question

I found this formula (see link) that's supposed to calculate the length of each side of my polygon. But I end up with an negative size, my polygon has 16 sides and an radius of 24 cm. So how do I calculate how long each side should actually be?

https://i.stack.imgur.com/1G2gI.png

Answer 1

You've most likely used a calculator to compute $$ \sin(\frac{180}{16}) $$ and gotten $-0.967$, but that's because the calculator is using radians, not degrees. The thing you really wanted to compute was $$ \sin(\frac{\pi}{16}) \approx 0.19509032201 $$ which, when multiplied by 48 (i.e., twice the radius) gives you a side-length of approximately $ 9.36433545677 $ centimeters.

(You could also switch your calculator to "degrees" mode to get the same answer.) I hope this helps.