What is the Correct Electric Charge Force Diagram for a Single Charge?

[Kavorka]

I drew a force diagram of one charge with gravity downward, electric force to the right, and tension at 20 degrees left of +y. I summed the forces in the x and y directions:

Fy = Tsin20° - mg = 0

T = 0.1434 N

Fx = kq^2 / r^2 - Tcos20° = 0

q = 6.29 x 10^-12 C

The correct answer is 2.9 x 10^-7 C, though my answer is a multiple choice option so whatever I did wrong probably happens often. I'm not sure what exactly I did wrong, only that I believe q is supposed to be equal to 2Lsinθ√((mg/k)tanθ) through some derivation. Some pointers would be appreciated!

 

[TSny]

Fy = Tsin20° - mg = 0

T = 0.1434 N

Fx = kq^2 / r^2 - Tcos20° = 0

Did you use the correct trig functions?

 

[Kavorka]

Thank you! I mixed my sine and cosine up and I also didn't solve for q properly (didn't take square root of everything). Plugging everything back in I got the right answer.