Tongue pulls back slightly from the T position, blending into R. Sounds close to 'chr'.

Americans pronounce trips as TRIHPS (/trɪps/). In "trips", the "tr" cluster blends into a "chr" sound — a natural American English pronunciation. This is called the TR Sounds Like CHR, a small move that separates 'classroom' from 'native'. It comes out as TRIHPS. You'll hear it in sentences like "I always wear my seatbelt even on short trips".
Record yourself saying "trips" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 5 sounds. Explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the T position, blending into R. Sounds close to 'chr'.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Press your lips together to stop the air, then release. No vocal cord vibration.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "trips", the "tr" cluster blends into a "chr" sound — a natural American English pronunciation. /t/ shifts toward /tʃ/ ("ch"), so TR sounds like "chr".