Damon
Hey Bob Would be good if we had a more complete description of how this is hanging. No idea now what the angles θ1 and θ2 are referenced to. I'll make an assumption that the angles are relative to horizontal If the angles are relative to a vertical, just swap cos and sin in all my calculations. remember that tanθ2 = sinθ2/cosθ2 If the angles are relative to something else, we need more information. Let T1 and T2 be the tensions in the cords Summing forces in the horizontal direction to zero shows that the horizontal components of each string tension must be equal T2 cosθ2 = T1cosθ1 T2 = T1cosθ1 / cosθ2 summing forces in the vertical to zero with up as positive 0 = T1sinθ1 + T2sinθ2 - mg subbing in T2 from earlier 0 = T1sinθ1 + (T1cosθ1 / cosθ2)sinθ2 - mg mg =T1(sinθ1 + cosθ1sinθ2 / cosθ2) mg =T1(sinθ1 + cosθ1tanθ2) T1 = mg / (sinθ1 + cosθ1tanθ2) T1 = 5.1(9.81) / (sin37.87 + cos37.87tan61.11) T1 = 24.5 N