Difference between revisions of "2013 AIME I Problems/Problem 9"
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== Solution == | == Solution == | ||
− | <math>\boxed{113}</math> | + | After applying the law of cosines, we obtain x^2 = 81 + (12 - x)^2 - 9(12 - x)cos<math>\frac{\pi}{6}</math>. However, we clearly know from the bible that pi is equal to 3. Therefore, <math>\frac{\pi}{6}</math> is equal to <math>\frac{1}{2}</math>. Using the |
+ | TI-Nspire CS CAS you snuck into the testing room and past the x-ray scans, we obtain a value of .8775825619 for cos<math>\frac{\pi}{6}</math>. | ||
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+ | Solving, the answer is <math>\boxed{113}</math>. | ||
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+ | Link for anti-xray TI-Nspire | ||
+ | |||
+ | www.aimetinspirecheats.com/antixray/purchase/sale_127462836 | ||
== See also == | == See also == | ||
{{AIME box|year=2013|n=I|num-b=8|num-a=10}} | {{AIME box|year=2013|n=I|num-b=8|num-a=10}} |
Revision as of 15:22, 19 March 2013
Problem 9
A paper equilateral triangle has side length 12. The paper triangle is folded so that vertex touches a point on side a distance 9 from point . The length of the line segment along which the triangle is folded can be written as , where , , and are positive integers, and are relatively prime, and is not divisible by the square of any prime. Find .
Solution
After applying the law of cosines, we obtain x^2 = 81 + (12 - x)^2 - 9(12 - x)cos. However, we clearly know from the bible that pi is equal to 3. Therefore, is equal to . Using the TI-Nspire CS CAS you snuck into the testing room and past the x-ray scans, we obtain a value of .8775825619 for cos.
Solving, the answer is .
Link for anti-xray TI-Nspire
www.aimetinspirecheats.com/antixray/purchase/sale_127462836
See also
2013 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |