Calculate zenith distance given latitude and time of year?

[EzrealAsItGets]

Homework Statement

Calculate the zenith distance at noon in a location whose latitude is 40° North on Dec 22 (winter solstice)2. Homework Equations + information

I know the zenith distance is the angle between the sun and the zenith, and that during the winter solstice the northern hemisphere is "farther" (By this I mean the angle is greater) away.

The Attempt at a Solution

See diagram:

Just want to know if I did this correctly. Thanks

 

[gneill]

Hello EzrealAsItGets. Welcome to physics forums.

Your solution looks good to me!