ACT Math Practice Question #1290 (Medium (31)) | Test Citadel
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ACT Math Difficulty: Medium (31)

Digital ACT Math Practice Question #1290

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In $\triangle XYZ$, the measure of $\angle X$ is $45^\circ$, the measure of $\angle Y$ is $30^\circ$, and the side opposite $\angle Y$ has length $10\sqrt{2}$. What is the length of the side opposite $\angle X$?
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Law of Sines: $x = 10\sqrt{2} \times (\sin(45^\circ) / \sin(30^\circ)) = 10\sqrt{2} \times ((\sqrt{2}/2) / (1/2)) = 10\sqrt{2} \times \sqrt{2} = 20$.

Masterclass Solution & Distractor Trap Analysis

Apply the Law of Sines: $\frac{x}{\sin(X)} = \frac{y}{\sin(Y)}$. Here $X = 45^\circ$, $Y = 30^\circ$, and $y = 10\sqrt{2}$: $$\frac{x}{\sin(45^\circ)} = \frac{10\sqrt{2}}{\sin(30^\circ)} \implies \frac{x}{\sqrt{2}/2} = \frac{10\sqrt{2}}{1/2...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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