Reconstructing Kite Position and Rotation from a Single Camera Image

velcrome
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Image a kite (1 m wide, 3 m high, both crossing at a third of the height).
Also imagine a digital camera (800x600 pixel with a horizontal field of view of 45°).

After launching the kite a photo is taken with the camera.

How can I easily calculate the exact position *and* rotation of the kite in a vectorspace defined by the camera at the moment the picture was taken?
I tried with trigonometry but failed. I assume there is an easier way with matrices but i don't know how. I appreciate any help.

*velcrome
 
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??Given what information?
 
there are four corners of the kite with precise pixel values in the picture.

and of course, the dimensions of the kite and the specifications of the camera is known.
 

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