Calculating distance from center of mass of two stars in a binary system 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?
It actually doesn't really matter: the angular separation is sufficiently small that you can use the small angle approximations $\sin \theta \approx \theta$ and $\tan \theta \approx \theta$ (where $\theta$ is in radians). In both cases the next term in the Taylor series is $\mathcal{O}(\theta^3)$ and the effect on the answer of dropping this and all subsequent terms of the Taylor series is in most realistic cases going to be utterly dwarfed by the uncertainty in the distance.