Define trigonometric ratios for acute angles using right-triangle similarity.
Choose the correct trigonometric ratio from the known and unknown sides
Problem
A right-triangle side-finding setup gives the side opposite an acute reference angle and asks for the hypotenuse. State the trigonometric ratio that directly connects those \(\text{two}~\text{side}~\text{roles}\).
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What this problem is really about
The correct trig function is the one whose definition contains both the known and requested side roles. We’ll inventory those roles, compare them against opposite-over-hypotenuse, adjacent-over-hypotenuse, and opposite-over-adjacent, and use the single direct match to form the equation.
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