A 155-N sign is supported by two ropes. One rope pulls up and to the right 26.5° above the horizontal with a tension T1, and the other rope pulls up and to the left 49.5° above the horizontal with a tension T2, as shown in the figure. Find the tensions T1 and T2.

Answer 1

T1*Cos26.5 - T2*Cos49.5 = 0
T1*Cos26.5 = T2*co49.5.
T1 = 0.73T2.

T1*sin26.5 + T2*sin49.5 = 155.
Replace T1 with 0.73T2:
0.73T2*sin26.5 + T2*sin49.5 = 155.
0.324T2 + 0.760T2 = 155.
1.084T2 = 155.
T2 = 143 N.

T1 = 0.73*143 = 104 N.