Calculate width of rotated image

[Lemmes]

Edit: Should this question rather be asked in the ImageMagick Repo?

Hello,
I need to recalculate values of worldfiles for arbitrarily rotated images without having to open the rotated image and read out the actual width.
Say we have a square image with 10000 px width and height that's being rotated clockwise 1.422346555 rad. Calculation of the new dimension should be easy enough:

var newLength = Math.Sin(1.422346555) * 10000 + Math.Cos(1.422346555) * 10000;
Console.WriteLine(newLength);
// returns 11369,066856491

Of course there is no hundredth of a pixel so it has to be rounded up. But actually the rotated image is 11372 instead of 11370 pixels wide. Another image 5000 px wide resulted in a 5686 px wide rotated image with the same angle - which is one extra pixel after rounding up.

So the question is: how does ImageMagick calculate the dimensions of a rotated image?
Thanks for your patience, Bernd

[Lemmes]

Answered here