I'm working on a double pendulum problem where I have to find a specific angle for implementation in MATLAB. I can find the angle that I need with basic trigonometry, but I was hoping that there is a fast and efficient way to find the angle with some kind of trick.
The angle I am looking for is
theta2 and all the labeled parameters are given.
Note that $\alpha$ can rotate over its entire range so that $0 \leq \alpha \leq 2\pi$.
Also the length of $R$ is determined from user input x-y coordinates (intersection of $R$ and $L_2$) so thoe coordinates are also known.