Right-Triangle Tangent Ratio (TOA)
Also known as TOA · SOHCAHTOA tangent
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TOA: Tangent is Opposite over Adjacent — the ratio to reach for when the hypotenuse is unknown. It rules angle-of-elevation problems: stand 50 m from a tower, sight its top at 31°, and the height is 50 × tan 31° ≈ 30 m. Solving for the angle uses arctan on the principal branch, which for two positive legs always lands in the acute range 0°–90° — no ambiguity.
Right-Triangle Tangent Ratio (TOA)
Where
- = Acute angle
- = Opposite side
- = Adjacent side
Missing one of these? Work it out first, then come back
- Acute angle — Right-Triangle Sine Ratio (SOH), Right-Triangle Cosine Ratio (CAH)
- Opposite side — Right-Triangle Sine Ratio (SOH), Law of Cosines
- Adjacent side — Right-Triangle Cosine Ratio (CAH), Law of Sines