Define trigonometric ratios for acute angles using right-triangle similarity.
Write the sine ratio for an acute angle in a right triangle
Problem
Relative to angle \(θ\), the opposite side has length \(3\) and the hypotenuse has length \(5\). Apply \(\sin(θ)=\text{opposite}/\text{hypotenuse}\) and write the resulting ratio.
Big Picture
What this problem is really about
Sine is built from two side roles relative to the stated acute angle. We’ll recall opposite over hypotenuse, assign those roles before using the numbers, substitute in numerator-denominator order, simplify if needed, and check that a right-triangle acute-angle ratio lies between zero and one.
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