Declination of the Sun

"It's gonna be a bright, bright sun-shiny day!"

Words to Begin With

A Quick Lesson in Basic Geometry

Diagram A

In Diagram A above, CD and AB are parallel, intersecting EF at G and H, respectively. Congruent (same) sets of angles are: 1, 3, 5, and 7; and 2, 4, 6, and 8. This is because opposite angles (ie: 1 and 3) are congruent (which is true for any 2 intersecting lines), and because same-side angles of parallel lines (ie: 3 and 7) are congruent.

I will refer to this as the SS (Same-Side) theorem.

And the Rest is Simple Mathematics...

Honest, I'm not kidding about this! I couldn't do these for the longest time, but I finally figured out how and where I went wrong: I was trying to make these problems a lot harder than they were! Just relax; they aren't that hard. Take it from someone who knows.

Three Possible Cases

Important Note: If you are given information about D, and you know either L or A, you can get whichever of them you do not have.

Case 1.

Case 1.

Case 2.

Case 2.

Case 3.

Case 3.

How 'Bout an Example?

Suppose it is the first day of summer, and the sun is over 23.5 N, and you've just observed the sun at an altitude of 50 degrees over the S horizon. What's your latitude?

First, let's examine what we have as information.

Next, what can we infer?

Now, we solve for our latitude.