Define trigonometric ratios for acute angles using right-triangle similarity.
Write the tangent ratio for an angle in a right triangle
Problem
Relative to angle \(θ\), the opposite side has length \(3\) and the adjacent side has length \(4\). Apply \(\tan(θ)=\text{opposite}/\text{adjacent}\) and write the resulting ratio.
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What this problem is really about
Tangent compares the two legs relative to the reference angle, so order matters. We’ll identify the opposite and adjacent roles first, place them as opposite over adjacent, substitute their lengths, simplify, and confirm that the ratio has not been inverted.
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