Ham radio operators were not the only ones who are prone to put antennas in trees: Citizens Band operators and Short Wave listeners comes to mind.
As far as how the coax got up a tall tree, if its purpose was to connect an antenna up the tree to a radio in the house, something was used to get a light line (think fishing) over a limb high in the tree and back to the ground. Any number of things can be used, hammer, spinning reel, sling shot, bow and arrow, potato gun……… then a heavier line would be used pull the antenna and attached coax up.
It will be difficult to determine what the coax was used for without knowing what it was attached to at least on one end. If it was attached to a radio the “large phone jack” should be a PL 259 (Google PL 259) to see what one looks like.
Without the radio, the choices of the coax use could be narrowed down a little by examining the end in the tree. If it is attached to an antenna, the size and configuration of the antenna could give a hint to the radio band it was use on. Another step could be taken. If the coax is not damaged, and if the connection to the antenna is still good and the antenna still functions, there is test equipment that can be used determine the frequencies for which the antenna was used.
This equipment is a little pricey so your choices may be to find someone (think well equipped ham) or enjoy wondering what the wire did before you come on the scene.
Keep in mind Ham is short for Amateur radio operator. In my case amateur should be emphasized. The opinions expressed herein, therefore, should not be viewed as that of an expert.
WA4FRI