Equilibrium of a Particle: Determining Forces in Cables and F for a 4-kg Lamp

[hdp12]

Homework Statement

I am stuck on this problem for my mechanics class. Please help me.
Determine the force in each cable and the force F needed to hold the 4-kg lamp in the position shown. Hint: First analyze the equilibrium at B; then, using the result for the force in BC, analyze the equilibrium at C.
https://lh3.googleusercontent.com/kt-gKr9Ea2WBCZo1vfabhXjaFp6AXyXtYDveGu_WTEl8F9WJJz8O3Ls-ubIJQX4pC8frkQ=w1210-h506

Homework Equations

The Attempt at a Solution

https://lh4.googleusercontent.com/y0vOSzZ-_r7CDcQXvHqkG2BNlAdXrz7cw9PHh3iX1r_uTPHBnYcMMbqTYYlBC6b2lCNA6k0bOfLIgDx_r65ZUiGqc6U=w1210-h506
Please guide me to the correct course of action.
Thank you for your help

 

[Nathanael]

Is angle θ₁ (in the picture) unknown?

 

[DEvens]

Tidy is not a bad thing. Often if you will just tidy things up you can see your own errors.

Renaming everything is often quite confusing for everybody. Your diagram calls the angles theta 1, theta 2, theta 3. And you have renamed them, but I can't quite figure out what you renamed theta 1 as. And you seem to have called all the forces F with a bewildering array of subscripts, which don't seem to have made it to the diagram. What is Fyy? Or is that Fgy? What is ABy and why is it equal to Fyy? I can sort of guess, but I should not have to.

Where did the value 34.64 come from? Because it looks like you calculate 40N just a couple lines later for the weight of the lamp.

You didn't state the values of the angles in your problem statement, and suddenly you have values for them in your solution.

What does "if ignoring C" mean?

That's enough for now. Tidy it and see if you can' figure out how to follow the hints in the original problem.

 

[hdp12]

Is this correct? I tried to simplify my variables and I believe I got the answer.