ShmoopTube

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Here's your shmoop du jour...

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If sin (A) = 3/5 and x = 10, what is the length of y?

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And here are the potential answers...

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According to SOHCAHTOA, sin is opposite over hypotenuse.

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If sin of angle A is 3 over 5, then the ratio of sides x and z is 3 to 5.

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Since we're told that x equals 10, we can set up a ratio that looks like this. And we

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cross multiply to solve for z.

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We get 10 times 5 equals 50...and 3 times z as 3z. So now divide both sides

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by 3 and we get that z equals around 16.7. And now that we have two side lengths of a

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right triangle, we can use the Pythagorean Theorem to solve for y.

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So now we can just plug in our values.

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10 squared plus y squared equals 16.7 squared. 100 plus y squared equals 278.89. Subtract

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100 from both sides, and we get that y squared equals 178.89.

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Take the square root of both sides, and we get that y equals plus or minus 13.3.

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Sides can't be negative...

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...so the answer is 13.3. So it's A.

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