You can calculate the sun angle of any given time and date on any location here. Then it's just a matter of high school trigonometrie.

It's a lot easier to check it out in Google Sketchup. I've drawn the basic shape of your house (old and new) for you, all you need to do is play around with the shadow settings - time and date, and you can watch the shadows move.

The height above sea level doesn't make much of a difference, but the slight slope does. Haven't modeled this though.

And I sincerely hope your house looks better in real life than my model.

Frans
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Sketchup file here: Tilt house.skp