OK I thought about it for a few minutes and here's a more straightforward way to think about it.
Imagine the forces on the gondola. 9.8 kN straight down, then t1 to the upper left and t2 to the upper right. t1 and t2 both have a horizontal and vertical component. Since t1 = t2 (the angle is the same), the vertical component of each is 4.9 kN.
We determine the angle using tan theta = 100/170, so theta is about 30. sin(30) = 4.9 kN / t1. sin(30) is 0.5 so t1 = t2 = 9.8 kN.
The trick is to realize that though you have essentially two forces acting on the gondola: gravity, and the vertical component of the tension. However, the vertical component of the tension is really the sum of t1 and t2, each of which has a horizontal component that cancels out the other.