Electric Fields and Styrofoam balls

[glid02]

Here is the question:
Three identical small Styrofoam balls (m = 1.93 g) are suspended from a fixed point by three nonconducting threads, each with a length of 49.0 cm and with negligible mass. At equilibrium the three balls form an equilateral triangle with sides of 29.2 cm. What is the common charge q carried by each ball?

I set it up by taking two of the balls and making them into two back-to-back right triangles of the same size. I used the equation Fe=mgtan(theta) where theta is sin^-1(.146/.49)=17.335 deg. For this I got 5.909787*e-3.

Then I used the equation q^2=Fe(r^2)/ke, where r is .292 m.
For this i got q=8.108e-7.

I've triple checked everything and I'm fairly confident that this is the right answer for two balls, but I'm not sure how the third ball plays into the answer. It seems like it would push the two balls apart from each other a little more, which would diminish the charge I got when considering just the two of them, but I'm not sure how to go about finding the amount that the third ball would change the distance between ball 1 and ball 2. Any help would be awesome. Thanks a lot.

 

[Astronuc]

Each of two balls repels the third. If one draws a line between two charges, the third ball is repelled with a net force perpendicular to that line. Each ball is repelled from the equilibrium distance from the center of mass which would coincide with the center of the equilateral triangle.

Each ball sits at the end of thread at some angle. The lateral component of tension in the string (related to the weight of each ball) is equal and opposite the repulsive electric force. You seem to have done that correctly.

Treat the forces as vectors along the line of action, then determine the component acting opposite the tension in the thread.