Why is a chet with a patach at the end of a word pronounced "ACH" and not "CHA"? Example: מָשִׁיחַ
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Actually, the question is why it is spelt differently, and not why it is pronounced differently at all. If you wanted to say meshicha, you certainly could. That would be a different word, of course, though a related one. It would be spelt משיחה.
For words that end in -ach, orthographic convention has us conclude them with the chet. This is also the case for words ending in -'a (such as רקיע) and in -ah, where the final ה is consonantal (such as אלוהּ).
The reason for all of these is that the final vowel/consonant combination is not preceded by a phonological alef, but by a rounding off of the previous vowel. Hence, mashi(y)ach, raqi(y)a and elo(w)ah.