We study three point charges at the corners of a triangle. Their charges are q1 = +4.0 10-9 C, q2 = −2.5 ✕ 10−9 C, and q3 = +5.0 10-9 C. Two distances of separation are also given,

Question

We study three point charges at the corners of a triangle. Their charges are q1 = +4.0 10-9 C, q2 = −2.5 ✕ 10−9 C, and q3 = +5.0 10-9 C. Two distances of separation are also given, 
ℓ12 = 6 m and ℓ13 = 9 m. 
Find the net electric force on q3

1- Fnet, x (N) 
2- Fnet, y (N)

bobpursley · Answer

I agree you will have to do it in x, y directions.
I will set up the x direction, you can do the y.
F12x=k q3q1/9^2 * (4.5/9)

now notice the last term.That is Sine of the angle between the vertical from 3, and the direction of L13. Notice if the pt 3 had been directly over 1, then the x component would have been zero.
Now when you do the y component, your term will be cosine(arctan4.5/9), and you can convert that to a cosine(arccos xxx) as you know the vertical distance from the pyth theorm.