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grei
Posts:
132
Registered:
11/27/12


Re: Triangle ProblemLaw of Sines/Cosines does not work
Posted:
Oct 13, 2013 11:12 AM


This looks like a case in which there may be two solutions.
We can apply the "cosine law". Since b is opposite angle theta_2, b^2= a^2+ c^2 2ac cos(theta_2).
Now write that as a quadratic equation for c: c^2 2acos(\theta_2) c+ (a^2 b^2)= 0 and solve for c using the quadratic formula.
For certain values of a, b, and theta_2, there may be two distinct positive roots, in which case there are two distinct triangles having these properties.



