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What are the side length ratios for the $30^\circ$-$60^\circ$-$90^\circ$ and $45^\circ$-$45^\circ$-$90^\circ$ special right triangles?

Study flashcard from the deck Digital SAT Math: Algebra, Advanced Math & Geometry.

Answer

For $30^\circ$-$60^\circ$-$90^\circ$: $x : x\sqrt{3} : 2x$ (opposite $30^\circ$ is $x$, opposite $60^\circ$ is $x\sqrt{3}$, hypotenuse is $2x$). For $45^\circ$-$45^\circ$-$90^\circ$: $x : x : x\sqrt{2}$.

Explanation

These ratios are also provided on the reference sheet at the beginning of each SAT math module, but memorizing them saves valuable test time.

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