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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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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
paul726Aus*
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*us*
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*au*
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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