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?

Paresh Mar 25, 2020

#1**+1 **

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

CPhill Mar 25, 2020