To find the pitch dimensions (triangle), use the Pythagorean Theorem, which is A^2+B^2=C^2 (A,squared + B,squared = C squared).

As an example:
You have a 4'x4' bed, your roof is 2' high at center of bed. So your triangle (one half of your roof) has a base of 2, your hight is 2, so

2sq+2sq = Csq
4+4 = Csq
8 = Csq
square root of 8 = C
2.83' = C

You can do the same if you want to use inches.
24sq+24sq = Csq
576+576 = Csq
1152 = Csq
square root of 1152 = C
33.94" = C

That get's you a roof that is exactly two foot high by 4 foot wide, with a 45deg joint at the top.

But, I read your post that you want the whole thing to be 2 foot high at the center, so using the same formula, your A is still 2', but your B is 2' minus the height of your base box. To make it easy, say your base box is 1', therefore leaving you with a 1' high roof at the center.
So,
2sq+1sq = Csq
4+1 = Csq
5 = Csq
sqr of 5 = C
2.24' = C

Inches:
24sq+12sq = Csq
576+144 = Csq
720 = Csq
sqr of 720 = C
26.83" = C

NOTE: When your A&B lengths do not match, you will not have a 45deg angle at the top, which might be a problem with finding a T-Angle joint that has the angle you need.

If you need further help, let me know and I'll dimension it up in Autocad and post a pic.

have Thank you. That was extremely helpful. I worked 12-14 hrs shift and not wrote a follow up that was decided on saturday. I was going to post today a change in plans via my wife suggestion, but you beat me to the punch. Your answer and your time is much appreciated. Please forgive my delay with my posting.

After I showed her the above plan with the a frame roof versus a hoop house that would open up, she voiced she like the smoother round look since the garden is in our front yard. I part of the movement that's turning their grass into a garden, to something I can eat. I live in North Tx where the drought is alive and doing well.
So I placed 1/2" PVC pipe on top of the wood and inserted into 1/2" 3 way connector on all 4 corners. Then I cut a 90" piece of 1/2" pipe into 2- 45" pieces and have connected them in the middle with a 1/2" T connector. I placed both ends into the top side of a 3 way connector on each end. one side corner and connected the two T connectors with a 1/2 pipe for stability. The pipe shows tension , because the end rises approx 1/2" off the corner. i believed this will be remedy when I screw upright snap clamps to the wood to hold it place.
It will have a handle and a 3/4 snap clamp attached to 1/2 pvc pipe on one side so I can lift it up to open it to prevent over heating and get to the food. I will send a picture. You may have a better idea.
This look was acceptable to my wife and seem less expensive and time consuming. I glueing the base pipe to the 3 way corner to prevent slippage.
I can't figure out how to add more than one photo per post. So I will add the others per post.

AUSTIN

4th and last picture. different view.

2nd . it will open. Not snap down or hinges applied. NO plastic covering yet.

3rd picture. didn't hit submit button earlier. anyway different view.

Lookin' good! You might end up having to reinforce the roof in a couple areas. Keep an eye out for the plastic sagging between your two hoop walls, and also look for overall structure sagging at the hoops themselves. You have horizontal cross brace for the hoops at the top, but the only vertical bracing is the hoops themselves. Depending on if you get rain, snow, wind, ect is if you need to add additional support. Other than those thoughts, looks like you are on the right track.

On a side note, during the non-cold season, you can tie a stretch of grid fence (cow fence) over the frame and it makes a decent trellis for vine plants (if you plant any). But then you definitely would want to look at adding a vertical reinforcement section at the sides, part of the hoops.

Anyways, experiment away and have some fun with it. Make some artistic shapes out of the extra pvc, paint, and use as garden deco.