I have reduced a problem I'm trying to solve, to the following $4$ equations:
$$\cos(\theta) = \frac{A}{b+c}$$ $$\sin(\theta) = \frac{D-e}{b-c}$$ $$\sin(\theta) = \frac{c}{e}$$ $$\cos(\theta)^2 + \sin(\theta)^2 = 1$$ where only $A$ and $D$ are known.
I having a hard time solving this analytically. Is there an analytic solution to these equations or can a solution only be found numerically? Is there a(n) (easy) way to tell whether it is one or the other?