In a highly technical post like this I'm never sure how well I'm explaining it. I tried to keep things at the high school trig/algebra II level for this one. I've proofread it a billion times now but is there anything I can clarify?
I think I discovered a tiny problem in your 'relative proportions' formula picture.
you have
y' y
- = -
z' z'
in the first line. The z' on the bottom right should be just a z, right?
Other than that, this is perfectly clear, and I understood it even though I just came out of high school and haven't started college yet! Absolutely fantastic work!
Oops. Actually it's not a z' in the denominator in the second fraction, but a comma following the fraction bar. That's confusing; I have removed it. Thanks!