Your triangle example holds true for something being seen in the same spot in the sky, but if this is what really occurs, they also will look smaller over time. Are we experiencing this? Having said that, if something in the sky is staying in a visible constant position, but is getting visibly smaller, how do we conclusively know that this object is not just moving away from us in a direct opposite direction..?
I suppose I should reply, seeing how I've been quoted there.
First of all, if stellar objects, like galaxies, behaved exactly as described in the triangle example, then they would
not look smaller - just take two points lying at the opposite edges of some galaxy as the two vertices of the triangle with you at the third. If each of those distances did expand by the same factor, then the angular size of the object would stay the same.
As it stands, however, massive objects do not expand alongside the expanding space. With that in mind, they do indeed look smaller the farther you look. Take the same triangle as before, but increase only the observer-edge_of_a_galaxy distances - the angle at the observer's vertex gets smaller.
As
phinds mentioned, this "getting smaller" is unobservable in our time frame. But. We can still tell which object(e.g. a typical galaxy) is farther away than another by measuring their redshifts.
Having done so, we can indeed see that a galaxy farther away is of smaller angular diameter than a similar galaxy closer by.
The last bit, I'm guessing, is you asking if this effect couldn't mean that everything is simply receeding away from us, to which I can answer: yes. That's exactly the observation that got people thinking about some explanation that ended up being the Big Bang and the expansion of the universe. It is consistent with space expanding everywhere, which is the explanation that avoids thinking of us being the centre of the universe, which had been considered silly since, I don't know, 17th century?
Having said all that, you can very well disregard half of it, since the whole triangle example that I've been using seems only barely relevant in the light of the article
phyzguy linked to on the previous page. Apparently, the far away things(z>1 if I read that correctly?) look further apart than they should.
In other words, as much as I like my intuition that I was taking about up to this point, it would seem that it was false, at least for some cases(high redshift).
Now, I can barely read that article, it being mostly dry equations that I have hard time groking, so if anybody would be so kind and enlighten this poor soul as to the why does it happen, and how is it even possible?
I mean, if you were to take four cardinal points on the celestial sphere, and then observe them all increasing their relative angular separation the farther you look, then you end up with having more than 2∏ radians in a circle, no? Help?