How far does the sun cast a shadow on my house wall?

Nerd moment:

Was thinking of planting against a south facing brick wall and was wondering how far the shadow from the roof overhang would extend along the wall.

So........

My latitude: 30.4° N.
Earths tilt: +/- 23.5°

Summer Solstice:
90° - 30.4° + 23.5° = 83.1°

Vernal & Autumnal Equinox:
90° - 30.4° = 59.6°

Winter Solstice:
90° - 30.4° - 23.5° = 36.1°

My roof overhang is 13.75". How far down the outside wall of my house will the shadow be cast?




So on Summer Solstice:
13.75"/tan(90 - 83.1) = 113.62"

Vernal and Autumnal Equinox:
13.75"/tan(90 - 59.6) = 23.44"

On Winter Solstice:
13.75"/tan(90 - 36.1) = 10.03"




My wall is about 100" from the ground to the overhang, so the shadow on Summer Solstice will encompass the whole wall plus 1.65" horizontally onto the ground away from the wall.

Since today is the Autumnal Equinox, I took a photo of the shadow on my south-facing wall.

Trig works....looks pretty damn close to the calculated 23.44".