....How accurate are you when you eyeball the distance across your room in the funny farm? If you are anywhere close to the sun, you should have your room down to the thousandth of an inch.
The famous aviator Wiley Post, 1920ish, had lost one eye when young. He trained to estimate distances very accurately with one eye. Hence, with no triangulation. He would often win wagers in bars this way. It enabled him to pass the Airman's exam, which required good vision.
So I'll let that issue pass.
However, you are correct in that NotBat has not shown the total of the triangulation issue. There are several issues.
(A) How much does the Moon change in diameter, from the Supermoon to the minima, and why?
What does it mean, if an object in the sky periodically, and predictably, changes in diameter?
(B) From where might we stand, say in a couple of places, to measure the Sun and Moon over the course of a year?
This would be to find their distance from the Earth.
(C) We commonly measure the height of mountains on the Moon, and the depth of craters, using a form of simple triangulation. Measuring the spreading of the shadows as the Moon moves to a crescent.
Notbat, care to comment?
(D) Given that the terminator line moves precisely across the lunar surface over the course of a lunar day (27+ Earth days) and we measure heights on the Moon of objects as they approach that terminator, geometrically this is only possible if the Moon is a sphere like object.
NotBat claims the Moon is just a bright light?
(E) A lunar eclipse is when the Earth occludes the Sun, as viewed from the Moon. We will consider the trig involved in this, along with a quite interesting topic, after NotBat answers the above questions and issues. This topic is how we can
predict lunar eclipses.
Any scientific theory is affirmed if it predicts correctly. We have a model of elliptical orbiting masses in space, which we can use to accurately predict many things. All on the basis of a synergistic development of math, and orbital mechanics, over three thousand years. But you reject all of that.
No problem. We can step through the fundamentals.