Consider the triangle depicted in 1. Is there a straightforward (and non singular) way to compute $b$ and $\gamma$ given $a$, $\alpha$, and $\beta$?
Finding a side and an angle of a triangle with one side and two related angles
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geometry
trigonometry
triangles
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0What do those double strikes mean? (Could you not insert a visible figure?) – 2017-02-19
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0The strikes indicate that the lines are parallel. What do you mean by a visible figure? – 2017-02-19
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0Can't be done. We can compute everything for the lower triangle but only the angle to the right and the bottom side for the upper triangle. Is there no additional info? – 2017-02-19
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0@Jens, you are probably right. Another question which interests me: is it possible to express $\beta$ as a function of $b$ and $\gamma$? Or as a function of all four parameters $a$, $b$, $\alpha$, and $\gamma$? – 2017-02-19
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0No. The only connection between $\beta$ and $\gamma$ is that $\gamma$ cannot be $\ge \beta$ because then there wouldn't be an upper triangle at all, just two lines which don't meet. – 2017-02-19
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0I overlooked your second question, to which the answer is yes. If you know all parameters except $\beta$, you can compute it. This is because you know two sides and an angle of the total triangle, which means you know everything about that triangle, including the angle of its bottom right corner (call it $\theta$). Then $\beta = \pi-\alpha-\theta$. – 2017-02-19