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# Pythagorean Theorem

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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 m high poles which are 14 m apart. When he is standing on the rope 4m away from one of the poles, he is 3m above the ground. How long in meters is the rope?

Apr 19, 2021

#1
+33572
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See diagram below:

Use pythagorean theorem to calculate ?    and ??  below

sqrt ( 12^2 + 4^2)    +  sqrt ( 12^2 + 10^2) = rope length

Apr 19, 2021
#2
+115
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The triangle with the side length 4 also has a height of 15-3, which is 12. Using the Pythagorean theorem, the hypotenuse is 4sqrt10.

On the other hand, we can split the quadrilateral on the left into a rectangle and a triangle, and that triangle has a base of 14-4=10 and a height of 15-3=12. Using the Pythagorean theorem, we get that the hypotenuse of that triangle is 2sqrt61.

Therefore, the length of the rope is $2\sqrt{61}+4\sqrt{10}$

Apr 19, 2021
#3
+121002
+2

Let  the point  at  the  top of  the left pole =  (0,15)

Let  the point  where  the  tightrope  walker is  =   ( 4, 3)

Let  the point on the  top right pole = (14,15)

Using  the distance  formula.....the  rope  length is

sqrt  [ ( 4^2  +(15 - 3)^2 ]  +  sqrt  [ ( 14 -4 )^2  + (15 - 3)^2 ]  =

sqrt [  16  + 12^2]  +  sqrt [ 10^2  + 12^2]  =

sqrt [ 160  ] +  sqrt [ 244  ]   ≈  28.27  m

Apr 19, 2021
#4
+115
+3

I like how you assigned coordinates to each of the vertices! This is very useful for coordinate proofs! I should use that in the future

OofPirate  Apr 19, 2021
#5
+121002
+1

THX....I usually  see it  better if I can assign coordinates  in  a problem .....

CPhill  Apr 19, 2021