Each side of a regular octagon is y cm long find the distance in cm between any two parallel sides of this octagon

Hans007
Feb 7, 2018

#1**+1 **

We can fing this using some trig

We have a right triangle with one leg = y/2

And the angle opposite this side = 22.5°

And 1/2 of the distance between the parallel sides is the other leg....and the angle opposite this side is 67.5°

So....using the Law of Sines....we can find half of the distance as

(y/2)sin (67.5) / sin (22.5) = (y/2) ( 1 + √2) = [ ( 1 + √2) / 2 ] y

So...twice the distance is (1 + √2) y = distance between the parallel sides

CPhill
Feb 7, 2018