11-21-2004, 11:22 AM | #1 (permalink) |
Upright
Location: Houston
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Math Problem
Last week I entered a math competition and one of their questions was. There is a hexagon with each side with length of 5 cm. What is the total length of all of its diagonal. I was really put off by this question, but then I thought that diagonals would cut each other and make 90 degree angles each.
Then I know one side is 5 cm, and its a 90 degree angle, so it'd be like 45 45 90 triangles, in which the ratio is 1, 1, square root of two respectively. Doing then all the proportion and math, i got 15 multiplied by square root of two or approximately 21.213 Is there any math expert out there who can verify my answer, help is appreciated Thank you. Hope it all makes sense. |
11-21-2004, 11:40 AM | #2 (permalink) |
Insane
Location: Ithaca, New York
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not quite. for the diagonals that radiate from the center, they make angles of 60 degrees (360/6). there are other diagonals that don't go through the center. I believe there are a total of nine diagonals
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11-23-2004, 06:00 PM | #5 (permalink) |
Insane
Location: Wales, UK, Europe, Earth, Milky Way, Universe
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I havent done trigonometry for over 3 years.. lets see if it stuck...
lengthOfDiagType1 = 5 / (sin 120) = 5.7735 (From sin 120 = 5 / Hypoteneuse) lengthOfDiagType2 = 2 * sideLength = 2 * 5 = 10 count(diagType1) = 6 count(diagType2) = 3 (6 * lengthOfDiagType1) + (3 * lengthOfDiagType2) = 64.641 cm (to 3 dp) Could someone check that please, its very possible that i got it wrong hehe. No pythagoras here zen_tom P.S. sorry i listed it like a program, thats just what i'm good at...
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12-02-2004, 10:56 PM | #8 (permalink) |
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I get a different answer than welshbyte. The "long" diagonals are indeed 10cm long, but for the shorter ones I get 5*sqrt(3) or ~8.66.
I get this answer from the Law on Sines: x/sin(120) = 5/sin(30). The total length would be 3*10 + 6*(5*sqrt(3)), or ~81.96. |
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