In the first sentence, the article "the" is used before the noun "dog" to specify which specific dog is being referred to - the one that was tamed by man a long time ago. This article helps to clarify that the dog in question is not just any dog, but a particular one that had a specific experience of being tamed by man.

In the second sentence, the article "the" is used before the nouns "pity" and "living" to denote a specific feeling and a specific situation. By using "the," the author is indicating that the feeling of pity being experienced is specific to the context of the situation described, and the living arrangements being discussed are unique to this particular scenario.