I have a list of line lengths and angles, but only the angles between line $n$ and $n-1$, and I can't find a single expression to get the coordinate that works for all cases.
I tried $ \sum{\sqrt{\frac{L^2 -c^2}{\tan(\sum{\theta})^2+1}}} $ and similar expressions but they all assume triangles can be constructed for each out of straight line functions, which is not the case, any help is appreciated.
In the diagram below, $A$, $B$ and $C$ are three consecutive vertices of your polygonal. Suppose you know angles $\theta_A$ (made by line $AB$ with the $x$ axis) and $\varphi_B$ (angle between $AB$ and $BC$), as well as the coordinates of $A$ and $B$ and the length $L_{BC}$ of ${BC}$. The angle $BC$ forms with the $x$ axis is $\theta_B=\varphi_B+\theta_A-\pi$ and the coordinates of $C$ can thus be found from $$ x_C=x_B+L_{BC}\cos\theta_B,\quad y_C=y_B+L_{BC}\sin\theta_B. $$ You can then recursively compute the coordinates of all vertices, given the coordinates of the first two.