For example: I want to know the distance between Alpha Orionis (Betelgeuse) and Beta Orionis (Rigel). Is this possible? You only know the distance from Earth. May be this is a math problem and not an Astronomy question.
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$\begingroup$ Well, you need 3 coordinates of each body to determine their 3D-distance. The position on the celestial sphere gives you 2, then the third is distance. So yeah, it is possible. But please don't ask for the exact method, else that sounds too much like a homework-question. $\endgroup$– AtmosphericPrisonEscapeCommented Aug 25, 2016 at 11:32
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If you know the distance of each star from earth, and the angle between the stars, then you can us the cosine rule to find their distance from each other. See this for detail https://en.wikipedia.org/wiki/Law_of_cosines
