Find distance from center of equilateral triangle to edge in given angle

I need to find the distance from the barycenter of an equilateral triangle to the edge in a given angle.

Here's a little sketch:

Given the outer radius of the triangle, the angle and the rotation (assuming the rotation in the picture would be $0$), I need to find the distance from the point on the edge (marked as red in the sketch) to the center.

Any help is appreciated!

• Where do you count the angle from?
– user
Commented May 3, 2018 at 19:48
• Counter-clockwise from the right, so 30° would be orthogonal to the right side of the triangle. Commented May 3, 2018 at 19:51
• It would be much simpler to count it either from direction to a (certain) vertex or from the direction to the midpoint of a (certain) edge.
– user
Commented May 3, 2018 at 19:53
• I wouldn't know, really. I don't really have any idea on how to go about this. Commented May 3, 2018 at 20:43
• So you start the angle parallel to the bottom? Commented May 3, 2018 at 20:49

This expression works for your particular choice of the angle: $$d=\frac{R}{2\cos(\arccos(\sin(3\alpha))/3)},$$ where $R$ is the radius of circumscribed circle (I assume this was meant by "outer radius of the triangle").