ShmoopTube

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Here’s your shmoop du jour, brought to you by the length of a line.

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Although…we hear it’s been using supplements.

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Find the length of CE.

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Here's a little picture and we're looking for the length of this line right here.

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And here are the potential answers...

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We know right off the bat, for example, that triangle CDE is a 30-60-90 triangle.

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…and we remember that the sides of a 30-60-90

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triangle always have a ratio of x to x square root of 3 to 2x.

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It’s pretty obvious that DE is the longer of the two legs…

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…and even if we weren’t sure by eyeballing it, we know it has to be the side across from the 60…

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…so we can use that information to solve for CE, the hypotenuse.

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5 equals x square root of 3.

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We want to get x alone…

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…so we divide both sides by square root of 3…

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…and x equals 5 over the square root of 3.

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Our hypotenuse has to be 2x…so multiply that whole thing by 2 and we wind up with

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10 over the square root of 3. Of course, we have this thing about leaving

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square roots in the denominator… …so multiply both the top and bottom by

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square root of 3 and we have 10 square root of 3 all over 3…

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…which is answer B.

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We didn’t even need triangle ABC. Who knows why they threw that in here.

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