the law of cosines applies if you have an angle and its sides making it up, so say, if you had angle B and sides "a" and "c", angle B is made by those two sides, and thus the law of cosines would apply to get a missing side or angle.
in this case, we have two angles, B and C and only one side, so.... no dice on the law of cosines then.
now... .let's check closely, B is 66° and C is 28°... wait just a second!, that means A is 180 - ( 66 + 28 ), or 86°.
so then
[tex]\bf \cfrac{sin(C)}{c}=\cfrac{sin(A)}{a}\implies \cfrac{sin(28^o)}{11.6}=\cfrac{sin(86^o)}{a}\implies a=\cfrac{11.6\cdot sin(86^o)}{sin(28^o)}[/tex]
make sure your calculator is in Degree mode.
but "a" is roughly 24.6484428
