Tension Force Problem: Solving for T1 with x and y components using trigonometry

[Susie]

Homework Statement

A metal ball is suspended from the ceiling from two ropes. One of the ropes is at an angle of 55 degrees to the ceiling and has a tension of 400N. The other rope is at an angle of 75 degrees to the ceiling. What is the tension in the second rope? What is the mass of the metal ball?

Relevant Equations

400cos(55), 400sin(55)

I know I have to find the x and y components of T1 using 400cos(55) and 400sin(55) and I know that the x-component of T1 will = the x-component of T2 but opposite sign to give 0. But idk how to get there and what do to for the y-component. I think I found the weight, I think it’s 32.42g but I’m not too sure about that either.

 

[haruspex]

idk how to get there

I don't see your problem. You just explained how to get there, i.e. the x component of the second tension.

what do to for the y-component

You know the x component and the angle...

 

[Susie]

I don't see your problem. You just explained how to get there, i.e. the x component of the second tension.

You know the x component and the angle...

So basically it’s just
T1= <229,328>
T2=<-229,T2sin(75)>
Fnet=<229-229,328+T2sin(75)-(9.81)(32.42)>
?

 

[haruspex]

So basically it’s just
T1= <229,328>
T2=<-229,T2sin(75)>
Fnet=<229-229,328+T2sin(75)-(9.81)(32.42)>
?

Yes, except ...
Where did you get the 32.42 from? I don't think it is right. You should be finding this from these equations.
You can easily find T2sin(75) from the 229 figure. What is the relationship between the x and y components of T2?