Right-Triangle Cosine Ratio (CAH)
Also known as CAH · SOHCAHTOA cosine
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
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CAH: Cosine is Adjacent over Hypotenuse — the companion ratio to sine, tying an acute angle to the leg that touches it. A roofer reads it directly: a 6 m rafter pitched at 35° covers a horizontal run of 6 × cos 35° ≈ 4.9 m. Solving for the angle uses arccos on its principal branch (0°–90° here), which is single-valued because the ratio a/h must lie strictly between 0 and 1.
Right-Triangle Cosine Ratio (CAH)
Where
- = Acute angle
- = Adjacent side
- = Hypotenuse
Missing one of these? Work it out first, then come back
- Acute angle — Right-Triangle Sine Ratio (SOH), Right-Triangle Tangent Ratio (TOA)
- Adjacent side — Right-Triangle Tangent Ratio (TOA), Law of Sines
- Hypotenuse — Pythagorean Theorem, Right-Triangle Sine Ratio (SOH)