Relative to the positive horizontal axis, rope 1 makes an angle of 90 + 20 = 110 degrees, while rope 2 makes an angle of 90 - 30 = 60 degrees.
By Newton's second law,
- the net horizontal force acting on the beam is
where are the magnitudes of the tensions in ropes 1 and 2, respectively;
- the net vertical force acting on the beam is
where and
.
Eliminating , we have
Solve for .