Not sure if I have the correct angle and mass for this sum of forces

[dougiehazard]

Homework Statement

Balance the following face plate if the masses are as follows:A = 2.8 kg, B = 3.5 kg, C = 4.2 kg, D = 4.8 kg, E = ?(What angle and mass should E be placed to balance the other 4 masses

Balance the forces east-west:

3.5kg*sin45º + 4.2kg*cos30º - 4.8kg*sin30º - E*cosΘ = 0

E*cosΘ = 3.712 kg
balance north-south:

2.8kg + 3.5kg*cos45º - 4.2kg*sin30º - 4.8kg*cos30º + E*sinΘ = 0

E*sinΘ = 0.982
EsinΘ / EcosΘ = 0.982 / 3.712

tanΘ = 0.2645

Θ = 14.8º ◄
E = 3.712kg / cos14.8º = 3.84 kg ◄
If that's not right, then you want to balance the moments.
balancing east west:

3.5kg*0.35*sin45º + 4.2kg*0.315*cos30º - 4.8kg*0.6*sin30º - E*0.2*cosΘ = 0

E*cosΘ = 2.86 kg
and north-south

2.8kg*0.35 + 3.5kg*0.35*cos45º - 4.2kg*0.315*sin30º - 4.8kg*0.6*cos30º + E*0.2*sinΘ = 0

E*sinΘ = 6.55 kg
EsinΘ / EcosΘ = 6.55 / 2.86

tanΘ = 1.706

Θ = 59.6º ≈ 60º
E = 6.55kg / sin59.6º = 7.6 kg

 

[haruspex]

I assume you are asking which approach is correct.
Are we to understand that the plate is mounted vertically on a horizontal axis through the origin, and that the numbers in the diagram are distances of the masses from the origin?
What forces act where?

 

[dougiehazard]

forces are the weight id assume and yes the number are distances in the diagram

 

[haruspex]

forces are the weight id assume

Then why are you considering a horizontal balance of forces?
Does any other force act vertically?