the ski boat is traveling at 15 m/s and the tension in the rope is 80 N. If the boat does 3500 J of work on the skier in 54.6 m, what is the angle between the tow rope and the center line of the boat?

Answer 1

The horizontal component of the force towing the water skier is 3500/54.6 = 64.1 N. You don't need to know the speed to answer this.

The cosine of the tow rope angle is 64.1/80 = 0.801

Get the angle from that cosine.