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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.

oblique triangle

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.

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    The question is unclear. Are the lengths of $L_1,L_2,R$ known? – 2017-01-03
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    @Jack yes, those variables are indeed known. – 2017-01-03
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    I don't think $R$ is given. – 2017-01-03
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    @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. – 2017-01-03
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    @pseudoeuclidean $\beta$ was defined wrong in the first picture. I have updated it. It is the angle between the downward vertical and $R$ – 2017-01-03
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    @Ortix92 Yeah, I just missed that edit – 2017-01-03
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    @Jack correct, I will update the picture again – 2017-01-03
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    Take your time and make all corrections in one go. – 2017-01-03
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    @Narasimham it should be correct now – 2017-01-03
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    Have you tried [Law of sines](https://en.wikipedia.org/wiki/Law_of_sines)? – 2017-01-03

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Step 1: Since one knows all the three sides, one can find all the three angles of the triangle.

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.