Sun Shadow Length
The ground shadow a vertical object casts on level ground: shadow = object height / tan(sun altitude), so the shadow is height x cot(altitude) and the shadow-to-height ratio depends only on the sun angle. A 10 ft object under a 30 degree sun throws a 17.3 ft shadow (1.73 x its height); at a 45 degree sun the shadow equals the height, and a low winter sun throws one nearly three times as long. Use the winter-design sun elevation for the worst-case shade -- the case a solar-access, tree-planting, or building-setback study turns on. Level ground and a vertical object assumed; the sun path and terrain govern.
Formula and source
shadow_length = object_height / tan(sun_altitude); shadow_ratio = 1 / tan(sun_altitude) = cot(sun_altitude).
Sun shadow-length geometry (first-principles trigonometry), by name; the sun path and terrain govern.
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