My class assignment is to calculate the length and direction of the shadow my house casts at the winter and summer solstices at solar noon. My latitude is 40.60 N and 73.82 W and my house is 22 feet high.

This LINK will explain how to deal with this question and your calculations.

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Here is a calculator that should give all the answers you need: http://www.wsanford.com/~wsanford/shadow_length.html