Finding max. and min. daylight duration at a given latitude.

Question

Here's my question: Compute the maximum & minimum daylight duration at the latitude of Phila. PA. (39.9500◦N) in hours and minutes. Approximating to the nearest minute.

What would be the best way to begin this? Just to be clear, Im not looking for the solution just a starting off point, any advice would be appreciated.

Here's what I managed so far, from what I read online, it seems wrong. Does this maybe require spherical trig. instead?

Answer 1

HINT

The red circle (lateral view) in figure below is the parallel of Philadelphia. To answer your question you must compute what fraction of it is exposed to sunlight in the two cases.

EDIT

Here's a diagram that could help you, representing the red circle in the minimum daylight case. $OH$ and $OP$ can be computed from the previous figure, and from them you can get $\alpha$. Daylight duration (in hours) is then $\displaystyle24{\alpha\over180°}$.