Please review this answer and let me know my problem area. I need to use the law of sines to resolve and I keep getting different answers. If at all possible provide step by step instructions on how to solve.

asin(A)=bsin(B)=csin(C)asin(A)=bsin(B)=csin(C)

Which for this problem, results in the following formula to find the value of a:

a=sin(A)bsin(B)a=sin(A)bsin(B)

However, since A is unknown, the formula will have to be applied twice, once to find the angle measure of C using the known values of B, then once again to find the side length a. Once B and C are both known, their sum can be subtracted from 180to find A.

The Law of Cosines states that an unknown angle can be found using the values of the other two sides and the measure of the unknown side's angle. The formula is:

a2=b2+c22bccos(A)a2=b2+c22bccos(A)

Once again, though, the angle measure of A is unknown so that would have to be found first. This cannot be done using the law of cosines because finding an unknown angle using this method requires knowing all of the side lengths. Therefore, using this method would require starting with the law of sines to find A. It is predicted that using the law of sines throughout will be the easier method.

Solving using the Law of Sines

sin(C)=cbsin(B)=3015sin(20)sin(C)=cbsin(B)=3015sin(20)

sin(C)=0.684sin(C)=0.684

C=sin1(0.684)=136.84C=sin1(0.684)=136.84

Now we can find the measure of angle A:

18020136.84=23.16