What's the distance between the centroid of a scalene triangle and a point on its edge, at a given angle?

Question

Suppose we have a triangle where no sides or angles are equal (scalene triangle), but assuming we know all angles and lengths of the sides. How can you calculate the distance between the centroid and a point on its edge, at a given angle?

Here is a picture (x = distance, θ = angle)

Answer 1

It is given by x=r sec($\theta$-π/6). Where r is the shortest distance of the point from line .