I am confused on how to calculate the distances for each star in a binary system to their centre of mass. I am trying to solve it from a book I am reading which shows the solution but I do not understand the solution.
So the info I am given is:
A system is located at a distance D (in parsecs). The two stars orbit around their centre of mass. Star A has an angular separation of a (in arcsecs) and star B has an angular separation of b (arcsecs).
So now I am trying to find the physical separation of the stars to their centre of mass.
The book's solution (once converting to correct units) is:
Distance for star A = D tan(a) Distance for star B = D tan(b)
I don't fully understand why they use tangent here because when I draw out a diagram of this situation i seem to need to use sine not tangent.
Here is how I drew it:
Why do they use tangent function and not the sine function? Have I drawn my diagram correctly?