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?
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.