A 115-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 48.5° above the horizontal with a tension T2, as shown in the figure. Find the tensions T1 and T2.

Answer 1

T1[26.5o] and T2[131.5o], CCW.

T1*Cos26.5 + T2*Cos131.5 = 0
T1*Cos26.5 = -T2*Cos131.5
T1 = 0.74T2

T1*sin26.5 + T2*sin131.5 + 115*sin270 = 0.
Replace T1 with 0.74T2:
0.74T2*sin26.5 + T2*sin131.5 + 115*sin270 = 0.
0.33T2 + 0.749T2 - 115 = 0
1.079T2 = 115.
T2 = 106.6 N.
T1 = .74T2 = .74*106.6 = 78.9 N.