Force of Gravity & Coulomb's Law Force Question

[Medeiros]

Homework Statement

Two small spheres of 15 g each are suspended from a common point by threads of length 35 cm. Each thread makes an angle with the vertical of 20 degrees. Each sphere carries the same charge. Find the magnitude of this charge.
(The correct answer is: 0.58 μC)

Homework Equations

1) F= k|q₁| |q₂| / r²
2) SOH CAH TOA
3) F=ma

The Attempt at a Solution

I drew a picture of the 2 strings hanging from the same point and labelled the angles.
Knowing that F(g)=max on Y axis and = 0 on X axis,
I thought I could get the force of gravity on the two particles by

angle x g x mass
sin(20) x 9.81 x 0.015 = 0.05033...N
(I also did this another way by finding a vector from how much of the string on the Y axis as missing, and doing a ratio between that and the length of the string, which took a long time and turned out to be sin(20) anyway)
From there, I plugged that force in Eq.1:
q² = Fr² / k
so q = 0.56625 μC

Although it is close, I didn't round off anything to get that answer, and my answer still doesn't round off to the correct one.
I was just wondering if
1. Did I get the force the wrong way?
2. Is there an easier way to do it?
2. Is there another way to do this?

Thank you in advance

 

[mjc123]

You seem to be saying mg*sinθ = kq²/r². Is this correct?
Draw a force diagram. What is the magnitude of the tangential force tending to reduce the angle? What is the magnitude of the tangential force tending to increase the angle?

 

[Medeiros]

You seem to be saying mg*sinθ = kq²/r². Is this correct?
Draw a force diagram. What is the magnitude of the tangential force tending to reduce the angle? What is the magnitude of the tangential force tending to increase the angle?

Yep that is correct.

I THINK I drew the tangential force vectors tending to reduce the angle in my first attempt and made it equal to the force increasing the angle (the electric force) which was the same as sin(20)*g*m

If that's not it, I'm not sure what it is then

 

[mjc123]

Is the electric force tangential?