Shadow length is an object's height divided by the tangent of the sun's altitude: equal to its height at 45°, twice at 27°, ten times at 6°.

The ratio depends on altitude alone; the direction is opposite the sun's azimuth. At 45° a pole casts its own height; at 10° nearly six times it — which is the arithmetic behind winter shadows and the reach of sunlight into a room, and why the same window is a different room in January.

Sol draws it to scale for any object, any hour, and points it the way the shadow falls.