How would i accomplish solving this problem?

Question

Two small spheres, each with a mass m=5.0 g and charge q, are suspended from a point by threads of length L=0.30 m. What is the charge on each spere if the treads make an angle theta = 20 degrees with the vertical?

Answer 1

Well, just sum the forces! Briefly let us consider only one of those two hanging charges:
The only two forces acting on it are gravity and the electric force. Define our y axis parallel with the gravitational force and draw a free body diagram.
The angle between the forces will be the same angle the wire hangs at, therefore tan(20 deg) = Electric force / Gravitational force

Now, consider that the electric force = k*q1*q2/r^2. In this case, since q1=q2=q, the electric force = k*q^2/r^2, where k is Coulomb's constant = 8.988e9

Now substitute your gravitational and electric forces and solve!

For a little review, you may want to find the tension in the thread.

Hope this helps!