Can any mathematically inclined FE'r show me a trigonometric tangent function for the suns height above the equator for any location that isn't exactly 3000 miles from the equator?
http://theflatearthsociety.org/forum/index.php?topic=26936.0#.VIn0lNLF-Gc
Ahhhhh, the memories. This was one of the first of a many step journey to the conclusion of a flat-earth. It's easy to come here and be a round-earther when all you do is shout with your eye and ears plugged shut. However, when you start actually doing research and learning things, your world comes crumbling down.
First of all, I was talking about the sun. Second of all, I asked for a mathematically inclined flat earther, you know, someone that knows that trig functions apply to right triangles.
The maths can apply to any celestial object provided your measurements are accurate enough. Also, everyone chose the wrong hole to poke in the experiment. If the earth were round, then the distance would be measured to the point between the two participants; a location under the supposed round earth and therefore not give a truly accurate measurement of the distance to the moon/sun/bird/cloud/anythingYouSeeInTheSky.
It's amusing that when I first posted this, round-earthers were the ones lauding this as yet another proof against the claims of flat-earthers. Yet, years later when I reference the same post as a flat-earther, it's suddenly a deeply flawed experiment.
I'll give you a moment to contemplate the ramifications of Confirmation Bias and how it applies to your everyday life.
I wasn't there to point out the glaring problem the first time so don't blame me for other round earthers. You didn't mention at all in the experiment that the moon needed to be somewhere specific, it's not even implied. You also didn't finish the experiment so there's that. Basically, the experiment is highly unlikely to be done faithfully (since the chances of the moon appearing directly above a spot between you and your hooker is slim). By the way, you can do this experiment on a round earth but instead of using the arc distance between observers you would use the chord distance.
Anyways back to the op.
Apparently no one in either camp noticed the glaring error in your experiment when first proposed; maybe they were willing to accept your assertion that this was a valid test under your stated conditions (this was a bad assumption on their part), or maybe they were just too busy thinking of better -
and cheaper(!) - ways to employ a hooker. It turns out there's another basic error in it: even if we add the constraint that both observers and the sub-lunar point must be in a straight line so the math is valid, if the sub-lunar point is not
between the two observers, the the one nearer the Moon must use the supplement of their measured elevation angle instead of the angle directly, otherwise, the trig gives the wrong answer. Again. Oops.
The most interesting result is that you will arrive at different values for h (height to the Moon) depending on where your observations are taken. If you're both farther from directly under the Moon, the value for h will be lower than if you're both looking nearly straight up. This won't surprise you if you think about it; if the Moon were right on the horizon for the observer at A,then tan(a) will be zero, so, regardless of the value of d or tan(b) in the formula
h = d * ( ( tan(a) * tan(b) ) / ( tan(a) + tan(b) ) )
the value for h will always be zero[nb]For any finite d and finite, non-zero tan(b), otherwise the result is undefined.[/nb]!
It turns out that the calculated value for the height of the Moon converges on the radius of the Earth as you both get closer to looking straight up. If anyone actually carried out this experiment properly and with multiple geometries, it would provide strong evidence not only that the Earth was indeed spherical, but could give a reasonable estimate of its radius!
Oh, yes... there's a typo in the equation that says
(d * h/tan(a)) tan(b) = h
It should be
(d - h/tan(a)) tan(b) = h
This error wasn't carried through to the solution for h, so it's probably a simple transcription error when typing the post. I'm surprised no one noticed this - the units don't work even if you don't follow the details of the algebra; too busy thinking about hookers, I guess.