A vertical pole standing on level ground is looked at twice on the same day: first when the sun's altitude is 60°, and again when it is 45°. Compared with the first shadow, the second shadow is:

A pole of height h casts a shadow h·cot60° = h/√3 the first time and h·cot45° = h the second time, so the second is h ÷ (h/√3) = √3 ≈ 1.73 times the first. The height cancels, so the factor is the same for any pole. A factor of 3 belongs to the pair 60° and 30°, not 60° and 45°; comparing the altitudes themselves (60 ÷ 45) suggests 4/3; and the shadow lengthens as the sun sinks, so 'one third' has the change backwards.