When the sun shines through an open doorway, the beam passing just under the lintel will strike the floor at the greatest distance from entryway. If the sun is at angle A with respect to the horizon, the beam will strike the floor at the same angle.

The beam and a perpendicular line from the point on the lintel under which the beam passes to the threshhold of the doorway form respectively the hypotenuse and one side (H) of a right triangle. The remaining side of the triangle (X) is a line from the bottom of the arbitrary verticle line to the target across the floor.

The tangent of any acute angle (A) of a right triangle is the ratio of the length of the opposite side to the length of the adjacent side:

Tan(A) = H/X

If you rearrange the terms, you get:

X = H/Tan(A)

X represents the farthest possible distance from any point on the threshold at which light can strike the floor.