Name the chord tone
You can already grab the 3rd and 5th of a chord on the keys. Now say them out loud.
Chords are built by skipping letters. The 3rd of a chord is always two letters up from the root, and the 5th is always four letters up. That is true of every chord there is — major, minor, diminished, anything.
So the 3rd of any A chord is some kind of C, and the 5th is some kind of E. Only the accidentals change with the chord quality: A major has C♯, A minor has a plain C. The letters never move.
root → skip a letter → 3rd → skip a letter → 5th
A major: the 3rd is a C, sharpened to fit. The 5th is E.
Practise this in the trainer — it opens with this lesson the first time the concept comes up.