Question 1138233
Isosceles Triangle, angles 45, 22.5, 22.5 degrees;
The side 8 mm is opposite the 45 degree angle.
You want length of either of the congruent sides.
Use Law Of Sines, unless you can find another way.


in case it helps,  22.5 degrees is  {{{pi/8}}}.
{{{sin(pi/8)=sqrt(2-sqrt(2))/2}}}.


You already know  {{{sin(pi/4)=sqrt(2)/2}}}.


Radius:
{{{((sqrt(2-sqrt(2)))/2)(16/sqrt(2))}}}


{{{4*sqrt(2)*sqrt(2-sqrt(2))}}}