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?
+37146 See diagram below:
Use pythagorean theorem to calculate ? and ?? below
sqrt ( 12^2 + 4^2) + sqrt ( 12^2 + 10^2) = rope length
+115 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 $2\sqrt{61}+4\sqrt{10}$
+129852 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
