Calculate strength of the electric field at indicated point

[prokaryote]

Homework Statement

https://imgur.com/a/wpir4
[/B]
a. What is the strength of the electric field at the position indicated by the dot in the figure? Use the following values: q1 = 1.09 nC, q2=0.93 nC, d1=2.49 cm, d2=6.9 cm, d3 = 4.27 cm.

b. What is the direction of the electric field at the position indicated by the dot in the figure? Specify the direction as an angle with respect to the horizontal.

Homework Equations

E = (k*q)/r²

k = 9*10⁹ N*m²/C²

The Attempt at a Solution

I've tried to simply sum the electric fields, using the distance of the two hypotenuses calculated with the Pythagorean theorem:
(k*(1.09*10^-9 C))/(.0494297 m)² + (k*(0.93*10^-9)/(.0811436 m)²
= 4.015*10³ C

I also tried calculating the x and y components separately, then summing the vectors, but it took an entire page and the answer was wrong. I tried doing it two other ways, but I don't even know what I did. I'm so lost. SOS

 

[TSny]

Welcome to PF. You do need to use vector addition here because electric field is a vector quantity. So, your second approach is correct. Devil is in the details. Please show your attempt at getting the components.

 

[prokaryote]

Welcome to PF. You do need to use vector addition here because electric field is a vector quantity. So, your second approach is correct. Devil is in the details. Please show your attempt at getting the components.

Ok. I'm pretty sure this is totally wrong so I apologize in advance.

https://imgur.com/a/zsnkC

 

[TSny]

Basically looks good except for a couple of things. The symbol F is not really appropriate for electric field since F usually represents force.

You defined your angles $\theta_1$ and $\theta_2$ as measured from the y axis. So, when getting the x components, would you use the cosine or the sine of these angles? [Or, are you taking the vertical axis as the x-axis and horizontal as y axis?]

Also, think about the signs of the components.

 

[prokaryote]

Basically looks good except for a couple of things. The symbol F is not really appropriate for electric field since F usually represents force.

You defined your angles $\theta_1$ and $\theta_2$ as measured from the y axis. So, when getting the x components, would you use the cosine or the sine of these angles? [Or, are you taking the vertical axis as the x-axis and horizontal as y axis?]

Also, think about the signs of the components.

Nice!
I flipped the sin/cosine assignment and made one of the y-components negative. Got the right answer.
Thank you so much!

 

[TSny]

OK. [One minor thing, it's good to express answers to an appropriate number of significant figures.]

Good work!