On August $21$ at $9$:$00$ A$.$M$.$ solar time, what is the vertical shadow length $()$ for a window with a $6-$inch setback in Shreveport, LA$,$ if the window is rotated $15$ towards the east, and we need to calculate the surface azimuth?

Assumptions:

Latitude $()$: $32\mathrm{.}47$ N

Window dimensions: $4$ ft wide $($W$),6$ ft tall $($H$)$

Setback distance $()$: $6$ inches $(0\mathrm{.}5$ ft$)$

Overhang depth: $2$ ft

Distance above window: $2\mathrm{.}5$ ft

Declination $()$: $12\mathrm{.}3$

Hour angle $()$: $-45\mathrm{.}0$

Surface azimuth $()$: Calculate for $15$ east of south