A Mass Hanging From Multiple Strings

[Null42]

A mass of 6 kg is hanging from a string, named string 3. The top of this string is connected to to other strings, string one which goes straight to the left to connect with a wall, and string two which connects to the ceiling making a 40 degree angle between the ceiling and the string. The problem is asking for the tension of string 2.
The available answers are:

EDIT: Will try and provide a picture when possible.

a) 1.2 N
b) 11 N
c) 34 N
d) 3.5 N
e) 40 N


I thought I could solve the problem by considering each string a vector, representing the force of each. Since there is no movement, the sum of the Forces should equal 0.
So , T1+T2+T3=0

I figure the force of T3 to be the F_g, which should be 6 *9.8=58.8 N

Using this I then came up with the following
T1*cos(180)+T2*cos(40)+58.8*cos(270) = 0
and
T1*sin(180)+T2*sin(40)+58.8*sin(270)=0

I figured I could use the second equation most easily, since the sin(180)=0.

So, I came up with 0+(.643)T2+58.8=0
(.643)*T2=-58.8
T2=-91.44
Of course, this is nowhere close to any of the available answers, and I can't seem to wrap my head around any other way of doing it. Any help would be greatly appreciated.

 

[Doc Al]

T1*sin(180)+T2*sin(40)+58.8*sin(270)=0

I figured I could use the second equation most easily, since the sin(180)=0.

So, I came up with 0+(.643)T2+58.8=0
(.643)*T2=-58.8
T2=-91.44

Assuming your description is accurate, the available answers are way off.

Your method is perfectly fine. You did make a sign error, but otherwise your answer is correct. (What is sin(270)?)

 

[Null42]

Ahhh, yes, sorry, 58.8 * -1. Thank you for that. I guess I'll just have to discuss it with the teacher. Thanks!