ShmoopTube

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For a good time, solve this shmoopy question...

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For the right triangle DEF, F = 60° and DF = 10.  What is DE?

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And here are your potential answers...

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OK this problem is really testing one thing and one thing only...

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...whether we recognize that we have a 30-60-90 triangle here.

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But if we do recognize it, then we know that this angle is 90 degrees... F here is 60 degrees...

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and E here is 30 degrees.

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We should know that the ratio of the sides of a 30-60-90 triangle is 1 to square root

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of 3 to 2.

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If we label each side we have 1 here, square root of 3 here and 2 here.

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The question asks for the length of DE; well, we know that DE is to DF as square root of

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3 is to 1...

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DF has a length of 10 and

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the key equation looks like this:

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Square root of 3 over 1 equals DE over 10.

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Cross multiply and we have 10 times square root of 3 equals 1 times DE... or just, uh, DE...

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So the answer is B.

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