i would build up the right side some with either dirt or concrete. your deck of your mower is going to hang if it has much of a lip, so make as smooth a transition as possible. keep this in mind at the top as well, you would hate it if you built the ramp then the mower won't go over the threshold!

If you have room, I'd build the ramp to fit the profile. Assuming your shed is level the corresponding ramp from the threshold to the ground would have a parallelogram shape to have the ramp lip touch the ground along its length and have the ramp and threshold marry up. The sides of the ramp will be parallel but the lip and threshold will not be. The angles on your ramp support bracing will all be the same, it will be the lengths that vary.

Before you build the ramp you should check to be sure the deck clears the threshold as it enters the shed. One way to do this is to set two boards from the shed floor to the ground to approximate the ramp. Next with your tractor on flat surface measure the deck clearance to the ground and the distance between the wheels where they touch the ground. Cut a piece of 2 x 4 to this length and nail scraps to the ends so the board is the same height off the flat surface as the deck. Use this to check the ramp angles. If it slides up the boards and onto the shed floor without hitting the threshold you're good to go. If it bottoms out then time to readjust ramp angle. This is as close as you'll get to do a trial fit without the tractor.

You could determine the angle to make the ramp by the same principle. Assuming the bottom lip of your deck is flat, the lowest point on your mower is between the two wheels and the ramp will be longer than the wheelbase of your mower you can calculate the angle between the shed and the ramp that will cause the deck to strike. It will basically be an inverse tangent function (also called arctangent). Measure the distance between the two wheels, let's say it is 48". The point where the deck will come closest to the threshold should be at the midpoint between your wheels, 24", assuming the deck lip is the same height from the ground all the way around. Measure the height to your deck from this midpoint, let's say 4". Take the inverse tangent of this ratio, tan(-1)(4/24)=9.46 deg, where tan(-1) is arctangent. Now that tells you the relationship in angles between the two right triangles formed between the deck midpoint, the point on the floor at the midpoint and both wheels. The 9.46 is not your final angle but the angles in relation to the shed floor and ramp. To find the angle from the floor to the ramp you double the arctan angle and subtract from 180. 180-(2)(9.46)= ~161 deg. That would be the angle between the shed floor and ramp. So your formula would be something like 180 - (2)(arctan(y/x)), where y is the height to the lip of the deck at the midpoint and x is half the distance between the front and rear wheel.

Gosh--that stuff is why i failed algebra and the higher up stuff in high school! Whew!
I found, if he makes one board of the ramp longer than the other, and puts the longer board on the low side to the floor of the shed, that the machine could be run inside without catching the lip of the deck on the edge of the opening.
And the less steep the ramp-s the better chance he can run the tractor inside.