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A 30∘–60∘–90∘30^\circ\text{–}60^\circ\text{–}90^\circ triangle has fixed side ratios relative to the hypotenuse: opposite 30∘30^\circ is 12\tfrac{1}{2} the hypotenuse, and adjacent 30∘30^\circ is 32\tfrac{\sqrt{3}}{2} of the hypotenuse. With hypotenuse 1010, the side opposite 30∘30^\circ is 10×12=510 \times \tfrac{1}{2} = 5, choice A. Choice C, 535\sqrt{3}, corresponds to the side adjacent the 30∘30^\circ angle (the longer leg), not the opposite. Choice B is the hypotenuse itself, and D is too large; it never appears as a leg in a 30∘–60∘–90∘30^\circ\text{–}60^\circ\text{–}90^\circ triangle with hypotenuse 10. Alternatively, use sine: sin⁡30∘=12\sin 30^\circ = \tfrac{1}{2}. The opposite side equals sin⁡30∘×hypotenuse=12⋅10=5\sin 30^\circ \times \text{hypotenuse} = \tfrac{1}{2}\cdot 10 = 5. On the PSAT, memorizing special right-triangle ratios (30-60-90 and 45-45-90) yields quick solutions without calculators and reduces algebraic error. Recognizing when a triangle matches these special cases can convert a multi-step trig computation into a one-step ratio application, freeing time for more involved questions elsewhere on the test.