The sun never 'sets' on a flat earth. It goes out of view due to perspective. To calculate the height of the sun, you need to use the below math to take this fact into account.

No, Perspective wont make things appear to drop below the horizon.

It makes them get closer to the horizon, and appear smaller.

it is also completely impossible to calculate the height of something given only a single angle (or even 2).

It is effectively trying to solve a right angle triangle with just a single angle (other than the right angle).

This will give you the shape, but not the scale.

It will tell you the sun is somewhere along a line, but not how far along it.

The sun isn't special. If the formula works on the sun, then it should work for everything else with similar circumstances.

There is no condition here that the sun is so far away that paralax does not matter like there is for the RE case, so this should work for anything.

If I want to know the height of a building, I just note the angle to the top and then stick it in the formula and find that out.

But that shows a tiny building to be 5000 km high.

That can't be right.

Same for a fence, it says it is 5000 km high, but I can easily climb over it in a few seconds.

Something tells me your math is pure BS.

And as per usual, you just provide a bunch of math, with no justification at all, so there is absolutely no basis for this being based upon a flat Earth.

I'll work backwards from your number, and I'll ditch the row part of the cell reference, and I will ditch the conversion between degrees and radians (i.e. the trig functions will use degrees, not radians). I will also use Z=10000, 4Z=40000, Y=90, 4Y=360, to make some of the writing out easier:

So you have the height given by:

T=TAN(S)*E

But S is simply given by:

S=ATAN(R)

As you are limited between 0 and 90 degrees, then tan(atan(x))=x.

This means you effectively have:

T=R*E

with one layer of extraneous BS removed.

Then subbing in

R=P/Q

E=(40000/360)*(90-C)=(4Z/4Y)*(Y-C)=(Z/Y)*(Y-C)

Thus:

T=(P/Q)*

((Z/Y)*(Y-C)

)Subbing in

P=J+N

Q=D*0.5

T=

((J+N)/(D*0.5)

)*

((Z/Y)*(Y-C)

)T=2*(J+N)*(Z/Y)*(Y-C)/D

Then subbing in:

D=90-C=Y-C

T=2*(J+N)*(Z/Y)*(Y-C)/(Y-C)

T=2*(J+N)*(Z/Y)

So there goes a lot more of your extraneous BS.

Now, I'll just try and quickly work with (J+N) separately.

J+N=H+I+L+M

H=(E/4Z)*C

I=(E/4Z)*D

L=(F/4Z)*C

M=(F/4Z)*D

Then remembering from before that D=Y-C, this simplifies to:

H=(E/4Z)*C

I=(E/4Z)*(Y-C)

L=(F/4Z)*C

M=(F/4Z)*(Y-C)

And with that I can already see another layer being removed:

H+I=(E/4Z)*C+(E/4Z)*(Y-C)=(E/4Z)*(C+Y-C)=(E/4Z)*Y

Similarly:

L+M=(F/4Z)*Y

So J+N=(E/4Z)*Y+(F/4Z)*Y

J+N=(Y/4Z)*(E+F)

So subbing that back into T:

T=2*(J+N)*(Z/Y)

T=(2/4)*(E+F)=(E+F)/2

So that is now getting much simpler.

But what about E and F:

E=(40000/360)*(90-C)=(4Z/4Y)*(Y-C)=(Z/Y)*(Y-C)

F=(40000/360)*(C)=(4Z/4Y)*(C)=(Z/Y)*(C)

So:

E+F=(Z/Y)*(Y-C)+(Z/Y)*(C)

E+F=(Z/Y)*(Y-C+C)=(Z/Y)*Y

E+F=Z

Now subbing that back into T:

T=(E+F)/2

T=Z/2

Much simpler.

So why not do this as your formula to calculate the height of the sun based upon the angle:

Height=5000 km.

No need for any extraneous BS.

Or if you would like to pretend it is there, how about this one:

5000 km * (1+angle-angle).

It is effectively the same thing, your way is filled with more convoluted BS.

You know the height you want, and are simply wiping out the angle from the equation.

Why do you insist on making it so convoluted?

Is it so you can pretend that it might actually be complex math based upon reality, rather than BSing numbers?

Do you work in a sideshow somewhere where you "read people's minds" by asking them to pick a number then continually manipulating it (without them easily seeing the pattern) to then reveal what the final number is, even though there could only be one possibility for the final number?

So where is the FE based math?

All I see there is height=5000 km, a baseless assertion.

We can also experiment with the value of Z and get whatever height we want.

Column E & Column F shows the distance to the 90 Degree Sun

Column P shows the unit of your perspective

Column S shows the actual angle taking into account your perspective

Coulmn T shows the flat earth sun height

Column E shows the distance to the sub-solar point, based upon RE math.

Column F shows the distance to the closest point 90 degrees away from the sub-solar point, again based upon RE math.

Column P is 22.5, it doesn't show any magic "unit of perspective".

Column S shows the angle that the sun should be at if the sun was actually 5000 km above Earth, rather than the observed angle in column C. This is the angle you would expect due to the effect of perspective, i.e. this is the angle that you should be observing the sun at. The sun not being at this angle shows the FE model to be BS.

Column T shows your asserted, and unjustified height of 5000 km.