Why in musical notation may one notate the chord as dominant 7th, even though only the major triad of it is played?

Question

In this arrangement of "Moonlight sonata" the author notated most of the triplets with the chords they correspond to. One thing, however, is not clear to me. Why the first triplet in the 4th bar is notated with G#7 chord, even though only the first three notes of the chord are played, which constitute only the major triad G#? This is not accidental and can be observed throughout the arrangement.

I am not a professional and I am still learning music theory, so doesn't make a lot of sense to me, why one might notate a triplet as a 7th chord, which by definition consists of four notes?

Answer 1

Actually both Beats 1 and 4 which are notated as G#7 contain F#’s. On beat one it happens on the 3rd triplet and on beat 4 it happens one octave lower on the 1st triplet, both in the right hand.

Beat 1 is actually missing the 5th, D#, but omitting the 5th is fairly common in chords. Another thing to mention is beat 2 should be written as C#m/G# since the G# is played through the entire bar. As a matter of fact, this style of music is not usually presented with chord changes at all.