# Calculate angle with vertical in oblique triangle

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.

• The question is unclear. Are the lengths of $L_1,L_2,R$ known? – Jack Jan 3 '17 at 14:58
• @Jack yes, those variables are indeed known. – Ortix92 Jan 3 '17 at 15:01
• I don't think $R$ is given. – Narasimham Jan 3 '17 at 15:01
• @Narasimham it is given, it is calculated as the norm of the x,y coordinates of the intersection of $R$ and $L_2$. Those coordinates are user input. – Ortix92 Jan 3 '17 at 15:03
• @pseudoeuclidean $\beta$ was defined wrong in the first picture. I have updated it. It is the angle between the downward vertical and $R$ – Ortix92 Jan 3 '17 at 15:04

Step 2: Now let $\gamma=\pi-\alpha-\beta$. Then $\gamma+\theta_2=\delta$ where $\delta$ is the angle between $L_1$ and $L_2$, which is done in Step 1.