When I went hiking I noticed how the mountains look in different perspectives: • Higher mountains tend to look small when they are far away and do not appear to be as high from a very long distance.
• Another issue is that I wanted to climb the highest mountains (600 meters) and the lowest ones reached 300 meters. From a distance of 500 meters the mountains of 600 meters disappear from my angle of vision (why? If they are supposed to be higher than those of 300 meters, why are they not seen behind those of 300 meters). On the other hand, if I went a further 500 meters away, curiously, the 600-meter mountains could be seen next to the 300-meter mountains.

I would like to know the mathematics of this real problem, because I find it interesting to see objects such as mountains so high and imposing being seen in different ways depending on distance, height, etc.

The problem would be to determine what makes the 600-meter mountains disappear from my point of view, if I am at a point that is more or less 1 km away from the 600-meter mountains and 500 meters from the 300-meter mountains. Another thing is that already being at the top of the 300m mountains, without any problem the other higher mountains of 500mts, 600mts, 700mts etc. were visible without any problem. does it have to do with distance and height? then, what would be the formulas to establish the solution of these questions.
Another fact is that the mountains are not one after the other in a straight line, but that they have an angle from where I see them. has to do with that? But if they were in a straight line, I don't know if the same thing would happen or not, because there is something that does not make them visible from my point of view.

I did more or less some graphics and possibly some math.