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Say I have a car and a kind of trailer with one set of wheels, for the purpose of describing my problem. The trailer is connected to the car by a ball-pivot joint. If the trailer is kept perfectly level with the ball joint, the wheels stick through the ground. How can I calculate how much to rotate it so the wheels rest perfectly on level ground with the car? Please don't answer "Trial and Error." Thanks.

I won't do all of your work for you, but I will give you a tip. The answer is simple trig. Have a look at the attached graphic...

You know the value of hh (Hitch Height) and the value of th (Trailer Height). Subtract the two. That gives you the length of one side of a triangle. The distance from the hitch to the center of the trailer's wheels gives you the second side of the triangle. You know know the length of two sides of a triangle. Now you just have to apply simple trig to calculate the angle (theta). Once you get your formula right, then it will work to rotate the trailer to its appropriate position as the vehilce is moving across terrain as well.