when does an object cast a long shadow
The sun casts shadows which change dramatically through the day. The length of a shadow cast on the ground is proportional to the cotangent of the sun's elevation angle -- its angle θ relative to the horizon. Near sunrise and sunset, when θ = 0 ° and cot (θ) = ∞, shadows can be extremely long. If the sun passes directly overhead, then θ = 90 °, cot (θ) = 0, and shadows are cast directly underneath objects.