Digital ACT Math Practice Question #1290
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Law of Sines: $x = 10\sqrt{2} \times (\sin(45^\circ) / \sin(30^\circ)) = 10\sqrt{2} \times ((\sqrt{2}/2) / (1/2)) = 10\sqrt{2} \times \sqrt{2} = 20$.
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...
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