The three ropes shown are tied to a small, very light ring that is stationary. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. What is the magnitude of the tension T3 in the third rope, if T1 = 37.7 N, T2 = 90.9 N, and the lengths of rope 1 and 2 are 1.96 m and 0.260 m, respectively?