Here's a breakdown of the factors at play:
* Historical sound changes: The English language has evolved over time, and sound changes have led to the development of certain vowel pronunciations. In the case of "waste," "paste," and "taste," the "a" sound likely originated from a longer, open "a" sound in Old English.
* Spelling: The spelling of these words (with an "a" followed by "st" or "ste") is a strong indicator of the long "a" sound. This is a common pattern in English, where a long "a" sound is often spelled with "ai" or "ay" ("wait," "play"), "ea" ("great"), or "a" followed by "st" or "ste" ("waste," "taste").
* Borrowing: The word "paste" comes from Old French "paste," and "taste" likely evolved from a Proto-Germanic word with a similar sound. These borrowed words often retained their original pronunciations, including the long "a" sound.
It's important to note:
While the "a" in these words sounds long, it's not always a perfect "a" sound like in "fate." It often has a slightly more open sound, closer to the "a" in "father."
In conclusion, the long "a" sound in "waste," "paste," and "taste" is a result of a combination of historical sound changes, spelling patterns, and borrowing. It's not simply a matter of following a rule, but rather a complex interplay of linguistic factors.