Electric Fields, finding a charge (1 Viewer)

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I have a question about electric fields:

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 as if the third ball would push the first two apart from each other a bit more, maybe a distance of .292m*sin(30), and that would diminish the charge I got by a ratio of (.292*sin(30))/.292. I don't know if that made any sense but that's the only other thing I can come up with. Any help would be great. Thanks a lot.
 
54
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Disregard the whole distance of .292m*sin(30). That does not make any sense.
 
54
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anybody have an idea to set me on the right track?
 

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