OK---i have a problem.

you lie on a beach and watch a sunset. then you stand and watch it set again--you are higher and can see that supposedly.

my book says that you then use these values:

(your height)

(the time between sunsets)

then using the picture and the Pythagorean theorem, with as the distance between your eyes and the tangent to the earth from the second sunset, you get

or

but you remove because your height is insignificant compared to the radius of the earth and the term

then you use the number of hours in a day, the rotation of the earth in a day, and to find :

which solves to

then you can get from the picture and, substituting for in the first equation,

which when you plug in the values (like ) makes

The problem is in the fact that we replaced the value for the from the angle between the sunsets with the from the angle from the center of the earth. i cant figure out how that works.

Here is the picture: