Well, this is what we started out with. It doesn't look like there's much we can do, but the coordinates of point C can be found by dividing the figure into multiple 30-60-90 triangles.
Based on the proportions of a 30-60-90 triangle, we can figure out the length of each side in terms of w. The shortest leg is w, the adjacent leg is w√3, and the hypotenuse is 2w. Put it all together and you should get (w√3,2w).
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