So I'm trying to calculate the latitude of where I am via a few factors. My lesson says I need to know the following:

Question

The date of my measurements: 4/3/17
the time: 12:30
my height: 5' 10"
my shadows length: 4' 6"

It then says first, compute the angle of the sun when the photo was taken, a, given by

a = arctan (known height / length of shadow.
I got 1.2 but am not sure if its correct. The arctan of 1.2 is 50.19442891? is there anything else needed to figure this out?

Answer 1

Since the distances involved are minuscule compared to the size of the earth, all you really need to know is your height and shadow length.

And you are correct that arctan(1.2) = 50.19°

You have listed the time as 12:30, so the sun should have been almost directly overhead (90°). The angle of 51° indicates that you were at a rather northern latitude. If it matters, you can research how the angle of the sun at noon relates to your latitude.

Answer 2

Well my assignment is asking that I use the equation and info provided to estimate the latitude of Tempe, AZ. which according to google earth is about 33 degrees. so I'm not sure what I am doing wrong. should've posted that originally, sorry.

Answer 3

I expect this article will help:

https://astronavigationdemystified.com/latitude-from-the-midday-sun/

Since your time of day is 12:30 rather than 12:00, you will need to factor that in.

Answer 4

Thanks a lot that did help. on another related note, the second part of the question asks what would the length of my shadow be if I did this on June 21st (summer solstice). Wouldn't my shadow be non-existent because the sun isn't behind me, but directly above me?