3 Point Charge Coulomb's Law problem

[Kastner86]

Homework Statement

3 Point charges are fixed in place in a right triangle. What is the electric force on the +1.0 nanoC charge due to the other two charges?

Basically you have 3 charges in a right angle as decribed, let's call them A, B, and C. In the upper left you have A, +0.8 nanoC. 8cm directly below is B, -0.6 nanoC. To the right of B at unkown distance is C, +1.0 nanoC. the distance AC is given as 10 cm.

So what is the electric force on charge C?

Homework Equations

I know I need Coulomb's Law. F_E=k\bulletq1\bulletq2/d²

The Attempt at a Solution

so first i convert all charges from nanoC to C to make things easier so the charges are:

A= 8e-7
B=-6e-7
C=1e-6

then i use pathagreom's theorum to find the distance BC, which is 0.06m.

Then I draw all the Force components on point C.

First I solve for F_B using Coulomb's Law and get 1.5N in the -x direction.

This seems to fine. I get stuck when trying to get the forces between point A and C...

I can get the angles... sin^-1(0.06/0.1)= 37 degrees.

but i honestly have no clue what to do next, and have been scouring resources on the net for a solution and finally ended up here, still with no answer... please help!

 

[Kastner86]

hey thanks for everyone who looked at my question. i finally figured out the answer though! the net electric force on C should be 1.2 N at 28 degrees from the negative x axis