Suppose ABC is an equilateral triangle and P is a point inside the triangle, such that PA = 3 cms., PB = 4 cms., and PC = 5 cms.
Then find the length of the side of the equilateral triangle.

sqrt(25+12*sqrt(3)) = 6.77
I don't know how he came up with this number. I have a solution in the form of three ugly equations with three unknowns, which is technically solvable but ugly. I did this by setting up vectors from each vertex to the center, then adding the vector from the center to point P (which is unknown, 2-dmensional, labeled D). Squaring these the equations gives 3 equations with 3 unknowns: the length of a side, and the two components of D.

Posted by C.B. on 2003-12-19 17:12:18