Well, ain't this a purr-fectly interesting problem! Let's unknot this together, shall we?
First, let's find the tension in the inclined cable. We can use a little trigonome-"meow"-try here. Given the angle θ of 38.0°, we can use the formula: tension = force / cosine(θ).
Since the force acting on the cat burglar is 688 N, we can plug in those numbers and calculate the tension in the inclined cable.
As for the horizontal cable, we're in for a "purr-suit" of the right answer. Since the horizontal cable is - you guessed it - horizontal, there's no vertical component to consider. Therefore, the tension in the horizontal cable is equal to the force acting on the cat burglar, which is 688 N.
Lastly, the tension in the vertical cable. As the name suggests, this cable is pulling "fur-reely" hard on the cat burglar, keeping them from falling. Since there's no horizontal component, the tension in the vertical cable is equal to the weight of the cat burglar, which is 688 N.
So, to sum it up:
Inclined cable: "Tension, you're on a slant!" - calculate using cosine(θ) and the given force.
Horizontal cable: "Tension, you're perfectly aligned!" - equal to the given force.
Vertical cable: "Tension, you're holding up the fort!" - equal to the weight of the cat burglar, which is 688 N.
I hope I've helped untangle this feline-filled problem for you!