my music teacher states that to differentiate first from second inversion triads listen to where the perfect fourth is. 1st inversion it is on top second inversion on the bottom. the tonic note is not given. would i sing do me le for first inversion and do fa ti for second inversion?
Assuming the same pitch is in the bass for each chord, and assuming movable-do solfège, yes, "do me le" would be the first inversion major triad. The second inversion major triad, however, would be "do fa la" (not ti).
But I don't personally recommend this method, since it forces you to always hear the bass as tonic instead of learning to identify the root of each chord. In other words, movable-do solfège always uses "do" as its focus, and keeping the bass as "do" tries to force every triad into a do-based key, which isn't usually ideal.
Instead, I recommend singing these triads on your own using scale degrees: always sing the root of the chord as "1," the third of the chord as "3," and the fifth of the chord as "5." So for a C-major chord, C is always "1", E is always "3", and G is always "5," no matter what pitch is in the bass.
Try to sing these scale degrees in various inversions: sing "1–3–5–3–1," but also learn to sing "5–1–3–1–5," and so on. The more you do this, the more you'll begin to hear what these scale degrees sound like.
Then you'll start to develop the ability to recognize what chord member is in the bass whenever a chord is played for you. If it's "3" (the chordal third) in the bass, it's in first inversion; if it's "5," it's second inversion; and if it's "1," it's obviously in root position.