GSU Trades Geometry · Pattern B · Living Diagram

The Living Triangle

Drag any vertex. Every angle, length, rise, and run updates live. Switch between roof pitch, stair layout, and the 3-4-5 right triangle that every tradesperson carries in their head.

The trade secret hiding inside every right triangle

The Pythagorean theorem is a daily tool. a² + b² = c² — that's every rafter, every stair stringer, every diagonal brace. If you know any two sides, you know the third. If your triangle satisfies 3-4-5 (or 6-8-10, or 9-12-15), your corner is square.

Roof pitch is rise over run. A "6 in 12" pitch means: for every 12 inches of horizontal run, the roof rises 6 inches. That ratio determines rafter length, cut angles, and how snow loads.

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Side A (Rise)

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Side B (Run)

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Side C (Hyp)

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Angle θ

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Pitch

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3-4-5 Valid?

a² + b² = c² · drag a vertex to calculate

🥉 Bronze — Triangle dragged

🥈 Silver — All 4 modes tried

🥇 Gold — 3-4-5 achieved

✦ Platinum — 45° right angle hit

Ask GENO: "How do I use the 3-4-5 rule to square a corner on a job site?" or "What is the rafter length for a 6-in-12 pitch on a 24-foot span?" — GENO AI Tutor, 32 languages, 24/7.