Electic field question - geometry

[flythisforme]

I have a problem where I need to find the net electric field on a point due to 6 charges. I attached the diagram. It is a pentagon of 5 charges with a 6th charge in the center. Each side of the pentagon is 4 mm, and there is a point P on the center of one side. I found that the line from point P to point 1 of the pentagon is 4.99mm, using the law of cosines. I need to figure out what the angle is at point P from the line to the side of the pentagon (the one I marked with a question mark), so I can find the x and y components of this line. I am not sure if the line bisects the 54° angle at point 1. Can someone help me with this?

Thanks a lot. I really appreciate it.

 

[whozum]

Are you trying to find the field at point P? All the x components cancel by symmetry..

 

[flythisforme]

Yeah, but I need the angle there to find the y component of it.

 

[whozum]

If line P to 1 is 5, then use the law of sines.

$$\frac{sin(a)}{A} = \frac{sin(b)}{B}$$