I'll take a swing!

For starters, cos120 = -0.5

Assuming that a and A are the same value, we get the following:

a^2 = 400 + c^2 - 40c * cos(a)

400 = a^2 + c^2 + ac

c^2 = a^2 + 400 - 40a * cos(c)

a^2 = 400 + a^2 + 400 - 40a * cos(c)

<=>

0 = 800 - 40a * cos(c)

<=>

0 = 800 - 40c * cos(a)

<=>

800 - 40a * cos(c) = 800 - 40c * cos(a)

<=>

40a * cos(c) = 40c * cos(a)

<=>

a * cos(c) = c * cos(a)

<=>

a = c * cos(a) / cos(c)

<=>

c = a * cos(c) / cos(a)

And that's as far as I got I'm probably forgetting some trig rules. Do you know anything else about these values?