determine equilateral triangle's length using a point from the inside
A point P within an equilateral triangle has a distance of 4, 5, and 6 units respectively from the vertices. Determine the lengths of the sides of the equilateral triangle.
I was able to break it down into 3 triangles (coming from point P). So what I did was to use Cosine Law on those triangles and was able to get
2 sin 30 degrees x sin (60 - 2 theta) = -2/a
Am I on the right track. It seems that if I continue, I'd be getting 3 unknowns, 2 equations which is not feasible, unless I'm good at guessing. Do you have any other ways to solve this ?
Thank you in advance.