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Topic: Re: Triangle Problem--Law of Sines/Cosines does not work
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Posts: 132
Registered: 11/27/12
Re: Triangle Problem--Law of Sines/Cosines does not work
Posted: Oct 13, 2013 11:12 AM
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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.

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