Well, someone finally built the daylight application I had always wanted to build. (Not as pretty of course, and upside-down.) You can put in any latitude, longitude, and time of day and get the exact angle of the sun. And it graphically shows the sunrise and sunset times for every day of the year.
So I plugged in the coordinates (30°18’01″ N 97°44’50″ W) and the dates for the summer and winter solstice to get all the extreme angles of the sun in Austin, Texas.
First is the altitude. This is the angle off of the horizon. 90 degrees is straight up. We’re pretty far south, so on the summer solstice the sun gets up to 80.1 degrees.
The second is the azimuth which is the position on the horizon that the sun is directly above. It is measured in degrees off of North. So South is 180 degrees.
The diagrams below all show summer solstice in red and winter solstice in blue.
The first two diagrams just show the angles of the sun at sunrise, sunset and high noon on the two solstices. The next one down on the left shows a profile of our house and the shadow cast at noon on each of those days.
The three diagram on the right show a silhouette top view of our house and the angle of shadows at sunrise, noon and sunset. The gray four sided outline is our oddly shaped lot.

The big surprise for me is how little sun our south wall gets in the summer. I wish I had had an application that did this for me while we were designing the house. We might have made some adjustments to take advantage of the shade a little more.