The other morning walking up the street to Mad City Coffee, the sun barely crept over the top of the bare trees behind the houses. It was nearing noon and nearing the Winter solstice. I wondered how high (or low) did the sun go up from the horizon in my area, DC area.
I knew it was about 40 degrees latitude. I knew the angle of declination of the Earth’s orbit was 23 1/2 degrees. At high noon at the equator, when the declination was 0 degrees, the sun would be 90 degrees overhead.
Then, locally at noon, the elevation should be about (90 – 40 – 23.5), which equals 27.5 degrees. Pretty low, a bit below that of the 30 degree angle in a 30-60-90 triangle.
When I got the time, I searched and found this NOAA solar elevation calculator. Hah! I was pretty close.