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

Americans pronounce triathlete as TRAHY-ath-leet (/ˈtraɪˌæθlit/). In "triathlete", 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 TRAHY·ATH·leet. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The triathlete trains for swimming, cycling, and running".
Record yourself saying "triathlete" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 8 sounds. Tap a syllable to jump to its row, then 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.
Start with your jaw open wide and your tongue resting low and flat. Glide the front of your tongue up toward the roof of your mouth as your jaw closes halfway.
Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Place the very tip of your tongue slightly between your teeth. Blow air gently around it without voicing.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "triathlete", the "tr" cluster blends into a "chr" sound — a natural American English pronunciation. /t/ shifts toward /tʃ/ ("ch"), so TR sounds like "chr".
Stress falls on the first syllable, not the others. Stretch TRAHY — keep everything else short and quick.