ShmoopTube

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Here's your shmoop du jour.

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If sin(x) = 1/2, what is the measure of Angle x?

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And here are the options:

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Ok, so this question wants to know the measure

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of angle X.

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According to SOHCAHTOA,

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the sine is opposite over hypotenuse.

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So if sin(x) equals one over two, one is the length of the side opposite angle x and two

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is the adjacent side, or the hypotenuse. Using the Pythagorean theorem, we can solve

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for the length of the missing leg.

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1 squared plus the leg squared equals 2 squared. This simplifies to 1 plus the leg squared

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equals 4.

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Subtract 1 from both sides, and we get that the leg squared equals 3. Take the square

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root of both sides, and the leg equals square root of 3.

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This makes the ratio of the sides, 1 to the square root of 3 to 2, making this a special 30-60-90 triangle.

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x, the angle opposite the smallest side length, is the smallest angle, or 30 degrees.

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So it's A.

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