Size in relation to altitude.

I apologise for this, before anyone complains.

But it just occurred to me, gazing out of my window, about the size of any potential "UFOs" in relation to the distance they are from us.
What I mean is, how high would a suitably sized UFO (let's say, the size of a house) have to be, to be completely invisible from us during the daytime?

Now, I had a quick look around about this, and being fantastically poor at maths, I couldn't figure out a way of working this out. Some variation of Pythag', maybe?

I was just curious as to the sizes and such of any "UFOs" that we may see, or not see. Perspective, and such.

Any thoughts would be nice.

Basically, how high an altitude would a relatively small UFO have to be to be invisible to the naked eye?

It depends.

The human eye can detect a tiny speck in the sky if conditions are right. At night you can often see aircraft that are 50 km away, and perhaps further under good conditions.

The question is, what is the angular diameter of a dark speck against a sky background have to be before you can tell a bird from an insect from airplane, etc. My own crude experiments indicate that this is very roughly in the neighborhood of a a few milliradians, (1 milliradian = the size of a meter stick one kilometer away). I'd like to see the results or more carefully done studies with lots of subjects.

For example, the other day my son and I saw a dark spec in the sky that appeared to be rising slowly. I couldn't make out what it was with theh naked eye, but with cheap 10x binoculars I could easily see that it was several balloons tied together. I doubt that it was more than 1 km away.