# Trying to find an unknown point just with angles

This is my model:

What I do know:

1. A, B, C, which form an equilateral triangle
2. Mab, Mbc, Mac which are the middle points
3. Angles x and y, which are the angles formed by the segment from the unknown point to the medians' points and a perpendicular from the faces of the triangle (I put a square to represent it).
4. If needed, I can do my algorithm find the same angle "z", which is not represented on the model, but is the same idea that x and y, but with middle point Mbc

What I don't know:

1. The unknown point represented on the model

There is no restriction on where the unknown point can be in 2D space.

I couldn't find a formula to find the unknown point with just with internal angles of the triangle and the x and y angles. If you can provide some reference, subject or even some clue on how to solve this, I would be grateful.

-

Consider the Triangle with vertices $MAC$, $MAB$ and $U$ (the unknown). We know the length of the line from $MAC$ to $MAB$, and we know the angles $U-MAB-MAC$ and $U-MAC-MAB$. Hence we know everything about the triangle ($ASA$). We can then calculate the lengths using the sin law, from which you can find your point $U$.
@JeanK: Well, notice that angle $X$ can be decomposed as the sum of angles $U-MAB-MAC$, $B-MAB-MAC$ and $90^o$. Since we can find $B-MAB-MAC$ (it is 120 degrees) we see that $X-210$ is equal to angle $U-MAB-MAC$. – Eric Naslund May 28 '11 at 22:11