Flashcard 17 - Math Flashcard Set for the SAT Exam

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The correct answer is:

\(x, \,x\sqrt{3},\, 2x\) and \(x,\, x, \,x\sqrt{2}\)


Explanation:

In a \(30-60-90\) triangle, the smallest side (opposite the smallest angle, \(30^{\circ}\)), is \(x\), the second-smallest side (opposite the second-smallest angle, \(60^{\circ}\)), is \(\sqrt{3}x\), and the longest side (opposite the \(90^{\circ}\) angle) is \(2x\).

In a \(45-45-90\) triangle, the sides opposite the \(45^{\circ}\) angles are \(x\) and the longest side (opposite the \(90^{\circ}\) angle) is \(\sqrt{2}x\).

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