Question 133473
The law of sines only works for two sides and one angle if the angle is one of the non-enclosed angle.  See diagram.  If the 2 sides are a and b, and the angle is angle C, then the Law of Sines won't help you.   But if you are given sides a and b and then either angle A or angle B, the Law of Sines works just fine.


{{{drawing(400,400,-5,5,-5,5,
triangle(-4,-2,-.5,3,3.5,-1),
locate(-4.3,-2.3,A),
locate(-.5,3.5,C),
locate(3.6,-1.1,B),
locate(-2.8,1,b),
locate(1.8,1.5,a),
locate(-.3,-1.9,c)
)}}}

Let's say that the angle is angle A, side a is 9 and side b is 11.


The law of sines is:


{{{a/sin(A)=b/sin(B)=c/sin(C)}}}



{{{a/sin(A)=b/sin(B)}}}
{{{9/sin(55)=11/sin(B)}}}


{{{sin(B)=(11*sin(55))/9}}}


{{{B=arcsin((11*sin(55))/9)}}}



Then {{{C=180-A-B}}}, and you can calculate c by {{{c=(a*sin(C))/sin(A)}}}


I'll let you take care of the arithmetic.