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Having an understanding of Major Scale Theory and Major Triads will make this formation a simple execution. In fact, you would have probably come across this type of triad a long time before seeing it explained here.

Minor Triad: ROOT, m3, P5

So as for most chords we start with the root, then by playing the third of the major scale flat and the perfect 5th we have a minor triad.

As for any chord formation where the minor third shows in a pattern is irrelevant, as long as the bass or a chordal or melodic instrument does present it. If the minor third is not presented at any stage then there is nothing to indicate you have been on a minor triad. If you have played the the Major Third during the passage then you would have indicated it to be of the major variety.

Another way to look at this triad is too consider the minor scale being played from the root. You’ll find that the third is the naturally occurring one in that scale.

You see, a minor scale is created by having a Flat 3rd, 6th and 7th. You can also create a minor scale by considering the relative Minor scale mode to the Major.

This is the most simple triad to create. It is a Major Chord. You can use this triad as the basis of creating other chords by altering it on the fly.

Major Triad: ROOT, M3, P5

This is the 1st, 3rd and 5th of the major scale. It is a simple as that. On keyboard you may invert the chord to M3, P5, ROOT or P5,ROOT,M3 - these would be known as inversions. On guitar you may omit the 3rd in the first octave and play it in the second octave, it is also likely that you will repeat the ROOT and P5 an octave higher.

Things to know:
You will not always represent M3 in the first octave, and with ‘heavy distortion’ you will almost never use the 3rd in any octave.