Do you round earth indocs accept the figures what Hoppy has put up?
Those figures are pythagorean theorem.
Yes Hoppy. I just want to make sure that these round earth indocs accept these answers as being correct by their view and if not, I'd like them to say why not.
How much of a 1000 ft sky scraper would I be able to see if I was viewing it across the water from say, 50 miles away, assuming the earth was a globe?
You can do the math yourself. Use the Pythagorean theorem.
I'll just wait to see if I can get an answer. It doesn't matter if you don't want to do it.
At 50 miles you wouldn't be able to see it at all. Check this chart.
http://www.sacred-texts.com/earth/za/za05.htm
Hoppy says the chart used the Pythagorean theorem. Here is my explanation in full detail.
I will use the theorem of Pythagorean as well to calculate how much you will be able to see at a certain distance and what the maximum distance is at which you can see something.
Before we go on and calculate, we first need to determine some things.
We know the earth's radius is 6371 km or 3959 miles. I prefer km, so I will go ahead and calculate using the metric system.
In the picture I can see the Willis Tower (Sears Tower), which has a height 442 meters (total height of 552 meters with antennas).
Now for the distance across Lake Michigan we need to know the location. Looking into the source tells us that the picture was taken from either Indiana Dunes National Lakeshore or Mount Baldy. This is a distance of approximately 60 km. If we would be right across Chicago on the other side of Lake Michigan, this would be a distance of approximately 80 km. The latter is about 50 miles, the first one is about 37 miles.
The formula = c^2 = a^2+ b^2
The following diagram shows you what we're doing.

With Pythogerean we can calculate one side of a right angle triangle if we know only two. We know the radius of the earth. This is A. Side C is the radius + the height of the building. Side B is the distance between the viewer and the building(s).
The green line and the green A is the same as the red A and we will need to substract this later on.
We can calculate how much of the lower section of the building is falling behind the horizon. This is C^2 = 6371^2+60^2
C^2 = 40,593,241 sqrt of 40,593,241 = 6371.282. All we need to do is substract the radius and we have know how much of the tower is not visible.
6371.282 - 6371 = 282 meters. Since the Willis Tower is 442, we now know that we only see the top 162 meters.
We can also calculate the maximum distance at which the top would just barely be below the horizon. This is 6371 + height of the building = 6371,442 ^2 = 6371 ^ 2 + B^2
40,595,273.16 = 40,589,641 + B^2 ?
We just have to solve this
-40,589,641 at both sides and we are left with
5632.16 = B ^2
Therefore B = sqrt 5632.16 = 75 km that is 46 miles. So at a distance of 46 miles the top of the Willis tower is not visible. The antenna would still be, but that is so small that it is hard to see with the naked eye. With antennas the height is 552 meters and doing the same calculations except with 6371,552 tells us that you will need to be 81,5 km away or 50.64 miles. Right across Lake Michigan you would thus be able to see the antennas of the Willis tower using binoculars, and if the weather is clear.
But, from the place where the picture was taken 162 m of the top is still visible.