You have all the information needed. Hint: Analyze the forces acting at the point where the cords meet. What does equilibrium tell you about the net force in any direction?
From that you can see that the total force upwards has to be provided by the second chord. So you break the chord into horizontal components. by doing this you are turning it into a vector diagram(pic)
from this you can use triginometry to find the force being exerted up, which will be opposite the force down, which in turn is the weight.