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## Poles and Strings

Math brain teasers require computations to solve.

 Puzzle ID: #2356 Fun: (2.47) Difficulty: (2.29) Category: Math Submitted By: KevThaDrinkKilla Corrected By: javaguru

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?

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 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(1-x), 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!