A tightrope walker, who has a mass of 60.0 kg moves to the center of the wire, which causes the wire to sag and make a 6.0° angle with the horizontal, what is the tension in the wire?

You need to resolve the forces in two perpendicular directions. In this case resolving vertically will be the useful part..

The downwards force is the weight of the tightrope walker (W=m.g) which is 60 x 9.8 = 588N.

The upwards force comes from the vertical component of the tension in the wire. This is T sin 6 from each side, so 2 T sin6 in total.

The vertical forces are in equilibrium so upward force = downwards force 588 = 2T sin 6 T = 588 / (2sin6) = 2.8 kN