Is there some sort of formula for how much shade is cast?

I’m thinking about building a house, and if I put in a pool, big if, I want it to be shaded at least part of the day. I’m hoping part of the shade will be delivered by the house blocking the sun.

I’m trying to figure how close the pool needs to be to the house to be shaded. The house might be a courtyard set up, so house on three sides. Unfortunately, a good portion of the backyard is south, or maybe I’ll be glad about that in the end for some sun in the middle of the day, but the sun will hit some of the east and west walls I think.

Some things to know: we will be on slightly lower ground than the houses to the south and west of us. I live in FL (I think my latitude is around 29 degrees north of that makes a difference). House walls will be minimum 10ft on the interior, keep in mind florida does not have steep roofs. Time of year might matter? I’m not sure.

What else do you need to know?