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A "slackrope walker" is much like a tightrope walker except that the rope on which he performs is not pulled tight. Paul, a slackrope walker, has a rope tied to two $15\text{ m}$ high poles which are $14\text{ m}$ apart. When he is standing on the rope $5\text{ m}$ away from one of the poles, he is $3\text{ m}$ above the ground. How long in meters is the rope?

 Mar 25, 2020
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Note that we have  two  right triangles

 

The  one  on the left  has legs  of  5  and (15  - 3)   =  12

And  the  rope length of  this section is the hypotenuse and  its length is

 

sqrt [ 12^2  + 5^2 ] =  sqrt   [ 144 +  25 ]  =  sqrt [169 ]  =  13 m

 

 

And  the   one  on the right  has legs  of   (14 - 5)  =  9  and  (15 - 3)  = 12

And the rope length of this section is the hypotenuse  and its length is 

 

sqrt [ 9^2  + 12^2 ] =   sqrt [  81 + 144 ]  =  sqrt [ 225 [ =     15  m

 

 

So......the total length of the rope =   13  +  15  =    28 m

 

 

 

cool coolcool

 Mar 25, 2020
edited by CPhill  Mar 25, 2020

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