>>12857882regular pentagon, so sum of angles COB BOA AOE EOD DOC = 360 degrees
each of these angles is equal to 360/5 = 72 degrees
given radius 1 we can use the formula for the length of a chord (which CD is because it's a regular pentagon) formed by an angle 2*radius*sin(angle/2)
angle/2 is 72/2=36
sub in the values, we get 2*1*sin(pi/5) = 2*sin(pi/5)
using the sin(x)^2+cos(x)^2=1 formula we can then calculate what sin(pi/5) is
sin(pi/5)^2+((1+sqrt(5))/4)^2=1
sin(pi/5)^2=1-((1+sqrt(5))/4)^2
sin(pi/5)^2=1-(1+sqrt(5))^2/16
sin(pi/5)^2=1-(1+2*sqrt(5)+5)/16
sin(pi/5)=sqrt(1-(1+2*sqrt(5)+5)/16)
sub that back into the chord formula, we get 2*sqrt(1-(1+2*sqrt(5)+5)/16)
get the 2 under the sqrt, it becomes sqrt(4-(1+2*sqrt(5)+5)/4) and that's your answer
