the distance given の意味は？

私たちは普段、基準面からの距離を認識して、その物の位置が高いかどうかを判断します。しかし、高い、高くない、というのは、相対的な判断であって、特定の距離を指すことはありません。

そのカッコの中には、本来、距離が入ります。しかしこの場合、距離が何であるかは関係ないので、数字で表さず、「任意の距離」という言葉をカッコで挿入しているのです。

カッコなしで、次のように書き換えてもいいです。

extending far upwards, measuring some distance from the base to the top.

This is not a piece of advice to you I'm talking to myself for my practice of writing skills. when I referred to the word "high" on monolingual dictionary I found its definition thus. "extending far upwards, measuring (the distance given) from the base to the top." I suppose it would be a common sense that on this screen right crick of the mouse would lead Google Translation start to work. even if you have clicked "日本語に翻訳(T)" in the case English sentence wouldn't been translated into mother tongue. in dialog box "this page has been translated. option. return to the original page" is presented. in such case click option. select English in the box "language of this page" . select your mother tongue in the translation language box then click translate box. then you would be able to read in your mother tongue. the reason why the sentences isn't translated might be GT wouldn't be able to judge what language the sentence being required translating is because of mixture of the language. I suppose it'd be helpful for your language learning.