to calculate b and then plug this into Pythagorean theorem
to get a.
But even simpler: If you know that in right triangle sin A=cos B, then you have
cos B=sin A=a/c
from which you can easily get a.
(I guess that A is the angle opposite to the side a and B is the angle opposite to the side b - this is probably shown in the figure you did not show us. Am I right?)