Hello all, I am having trouble with a trig problem, and was hoping I could get some help. Here's an image that should make it easier to understand what I need to do.

I have the coordinates of the three points, A, B, and C for the blue triangle, and as such, I can find the side lengths and inner angles easily using Pythagorean's Theorem and the Law of Cosines. What I need to be able to do is this:

Given a new angle between Pt A and Pt C (where Pt B is the vertex), how much do I need to translate Pt B on the y axis to form this new angle. The new Pt B will have the same x value as the old Pt B, only the y value must change. Another way of looking at it is, what is the length of the Red line in the picture above? I've been trying to figure this out for the last day and I can't do it . Please help!

Thank you in advance!