Oh, less than half a degree? Really?

I'd love to see these *simple maths* you boast of. Please, enlighten us.

I see Tumeni already has, but I spent a while on this so rather than wasting that time I'll post this anyway:

So, we are at point A and we are looking at a building at point B.

If we are living on a ball and the building is perpendicular to the ground then it will follow the line BD and will be leaning away from us at an angle.

I've drawn a line EF, parallel to the line AC.

So the angle the building is leaning away from us is EBD which I've called 'x'.

I've also drawn the lines from A and B to C which represents the centre of the circle/earth.

The angle at which those two lines meet at C is ACB which I've called 'y'.

But because AC and EF are parallel you should be able to see that x = y.

So now all we need to know is the circumference of the circle and the distance between A and B.

The circumference of earth = 24900 miles

The distance AB for the Turning Torso building is 30 miles.

So 30 / 24900 gives you the %age of the circle which AB covers.

All you need to do then is multiply that by 360 to get how many degrees y is, and therefore x.

(30 / 24900) x 360 = 0.4337 degrees.

To prove my logic is sound, what if the building was a quarter of the way around the world?

24900 / 4 = 6225.

So what would the angle be?

(6225/24900) x 360 = 90 degrees

Which is what you'd expect, a quarter of a circle.

Because the distant city in the original post pic is 45 miles away from the camera. Let's just see how many *fractions of a degree* those buildings are SUPPOSED to be leaning away. We'll be waiting patiently for your presentation.

I'll leave that as an exercise for the reader now I've given you the formula although now I've given you the value for 30 miles you should be about do 45 in your head

(hint, it'll be 50% more, so times the 30 mile value by 1.5).

I'm not having a go but come on, dude, this really was simple maths. I've probably over-complicated things, Tumeni's explanation was simpler and better. The fact that it had to be explained to you shows that you really don't understand stuff as well as you think you do. I note that you are now floundering around saying "Aha, but the experts say it's not a perfect sphere!". Well you're right.

For example, the WGS84 datum identifies the longest diameter of an ellipse (semi-major axis) as 6,378,137.0 m. Next, the semi-minor axis is 6,356,752.3 m.

https://earthhow.com/shape-of-the-earth/Divide these values into one another and you get an amount of oblateness of 1.0034. Less than one third of a percent.

It's small enough to mean the above maths is close enough that the error is very small.

As I said elsewhere, a common mistake people make is to think that because a model is imperfect it is not useful.

The earth is not a perfect sphere but for the purposes of the maths above it is close enough that the margin of error is tiny.