Law of Cosines for SSA triangles
In most geometry courses, we learn that there's no such thing as "SSA Congruence". That is, if we have triangles $ABC$ and $DEF$ such that $AB = DE$, $BC = EF$, and $\angle A = \angle D$, then we cannot deduce that $ABC$ and $DEF$ are congruent.
However, there are a few special cases in which SSA "works". That is, suppose $ABC$ is a triangle. Let $AB = x$, $BC = y$, and $\angle A = \theta$. For some values of $x$, $y$, and $\theta$, we can uniquely determine the third side, $AC$.
(a) Use the Law of Cosines to derive a quadratic equation in $AC$.
(b) Use the quadratic polynomial you found in part (a) in order to find conditions on $x, y,$ and $\theta$ which guarantee that the side $AC$ is uniquely determined.
I have the quadratic equation in part A, letting z = AC I got $z^2-2xz\cos(\theta)+(x^2-y^2)=0$
What would I do for part B?
Thanks
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