You can check your value of c by using the Law of Cosines, with the original calyues of a, b and C.
c^2 = a^2 + b^2 -2ab cos C
c^2 = 460.32 +2141.84 -1986.34*0.8436
c = 30.44
That is not what you came up with. There appears to be something wrong with your initial angles. The law of sines does not agree with your angles A and B. If A > B, than you should have a > b
Perhaps Mathmate can explain the origin of the problem.
I have looked at the question, and confirm that there was an error in the previous calculations using the law of tangents. Following are results using the sine rule:
a = 21.46, b = 46.28, C = 32-28-30
The cosine rule gives:
c = sqrt(a^2+b^2-2*a*b*cos(C))=30.440833
The sine rule gives
If you draw the triangle, with C=32°, a=21.46 and b=46.28, you will see a skew triangle which shows obviously that B>90°.
So sin(A) has to be interpreted as 180 - arcsin() of the acute angle, which gives 125-16-58 (instead of 54-43-02 straight from the calculator).
I have not completed looking into the source of the error of my previous calculations. It may have to do with the interpretation of the atan() values. I will get back to you when it is done.
I apologize for the inconvenience.
I just took another look. The formula for the law of tangents should have been tan((A+B)/s)/tan((A-B)/2)=(a+b)/(a-b).
Previously I have not divided the angles by 2, hence the error.
I will try to make a corrected version and repost in the original post.
The correction to the problem using the tangent rule has been posted at the original post:
Sorry for the inconvenience so caused.
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