Why does the leading tone (G#) go to E rather than A in this example?
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If the G# had risen to A, the pause chord would have three As. It sounds better with all the notes of the triad, including E. It's not good for the leading note to fall, but here is a situation where making it fall like that is considered an acceptable compromise. Bach made the leading note fall in a lot of his chorale harmonisations.
As Tim says the leading tone has to lead to the root tone of the tonic (in major and minor) when in the discant (Soprano) or Bass. But in the final chord, it is often - in purpose to have a full 4 voices harmony - lead down to the 5th in Alto or Tenor.