Poles and Strings
Math brain teasers require computations to solve.
You have two vertical poles. One stands at 6ft. 6in, the other at 7ft. 7in. From the top of each pole tie a string to the bottom of the other pole.
At what height do the two strings cross?
HintIt doesn't matter how far apart they are
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Answer
42 inches.
You multiply the height of the two poles and then divide that by the sum of the two heights..
(78 x 91) divided by (78 + 91) = 42
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Comments
lil_thugsta
Mar 01, 2002
 cool!! 
vanz
Mar 22, 2002
 nice! 
Captbob61
Mar 22, 2002
 great one! 
peterbradfor
Mar 27, 2002
 Nice to see HOW you get the answer, but WHY does the method work? 
cathalmccabe
May 29, 2002
 Peter.. its to do with triangle geometry, try drawing it two different ways, one with the poles close together and one with them far appart. Try to see whats happening. You can get the height by using corresponding sides in a triangle... The ratios of the triangles are the same which is the key 
paul726
Mar 08, 2006
 I used an (x,y) graph. I placed the 91" pole base at (0,0), and the 78" pole base at (1,0). The strings were line segments whose height equalled 91(1x), and 78x. I set them equal and solved for x, then multiplied that by 78 to arrive at 42. 
Crazycriely
Oct 15, 2006
 hey thanks! lol i might need to know that for future homework. 
javaguru
Mar 03, 2009
 Very cool and creative. 
Awkward
Mar 26, 2009
 Lol I ended up breaking out the Sin rule to solve this one. Nice to see my approach was much longer than necessary
I liked your approach too Paul, I miss my highschool days with fun questions that were solvable by utilizing lines and cartesian coords 
Jimbo
Apr 22, 2009
 Let distances from poles to where ropes cross be a and b. Let height be h. a/h = (a+b)/91 and b/h=(a+b)/78. Equating (a+b) gives a/b = 78/91.
Since it clearly doesn't matter how far apart the poles are then let a = 78 , b = 91.
Now 78/h = (78+91)/91. h = 78x91/(78+91).
Excellent puzzle! 
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