Define trigonometric ratios for acute angles using right-triangle similarity.
Write the cosine ratio for an angle in a right triangle
Problem
Relative to angle \(θ\), the adjacent side has length \(4\) and the hypotenuse has length \(5\). Apply \(\cos(θ)=\text{adjacent}/\text{hypotenuse}\) and write the resulting ratio.
Big Picture
What this problem is really about
Cosine uses the adjacent leg, not merely any side touching the reference angle. We’ll identify the hypotenuse first, isolate the other touching side as the adjacent leg, substitute adjacent over hypotenuse, simplify, and use the expected zero-to-one range as a quick check.
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