Step-by-step Answer:
This is a problem of "three concurrent forces meeting at a point" and can be solved by
1. Triangle of forces
2. parallelogram of forces
3. resolving the forces into the x-y components.
Since you appear to be working on vectors at the moment, I will solve using the third method.
For three concurrent forces to be in static equilibrium (our case here), the sum of x-components must equal zero, same for the sum of y-components.
We will let the force on the left wire to be R, and that on the right be T.
Resolving forces in the x-direction,
Sum-X = -Rcos(20)+100cos(90)+Tcos(30)=0
Simplify to get T=Rcos(20)/cos(30).............(1)
Next,
Sum-Y = Rsin(20)+Tsin(30)-100cos(0) = 0
or
Rsin(20)+Tsin(30)=100 .................(2)
Substitute (1) in (2)
Rsin(20)+Rcos(20)sin(30)/cos(30)=100
Simplify to get
R=100/(sin(20)+cos(20)sin(30)/cos(30))=113.05 ........(3)
Substitute (3) in (2) to get T=122.67
