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There are two things you need to know. You need to know h - the height of the object that will cast the shadow (assume it's all vertical). And then you need to know the angle (theta we'll call it) of the sun with respect to the vertical object of height that will cast the shadow.

The higher the sun the higher the angle. In fact in some instances the angle theta can be 0 degrees at noon (depending on location and time of day and year) or almost 90 degrees when the sun is sitting on the horizon. Where do you get this angle? I believe that the US Navy publishes these angles or they may be on line.

Well once you know the angle and the height h, the length of the shadow x is a simple calculation, x = h tan theta, where tan represents the trigonometric function tangent in a right triangle.

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Q: How could you predict the length and location of a shadow for a particular time?
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