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

#2**+1 **

See the following diagram

The slackrope walker is at "E"

We can form two right triangles

One has a legs of (15 -3) = 12 and 5

Then the hypotenuse od this triangle = sqrt [12^2 + 5^2] = sqrt (169) = 13 = (DE)

This is part of the rope length

The other right triangle has legs of 12 and (14 - 5) = 9

The hypotenuse of this triangle is sqrt [ 12^2 + 9^2] = sqrt [225] = 15 = (BE)

This is the other part of the rope

The total length of the rope is (DE) + (BE) = 13 + 15 ≈ 28 ft

CPhill May 31, 2024

#2**+1 **

Best Answer

See the following diagram

The slackrope walker is at "E"

We can form two right triangles

One has a legs of (15 -3) = 12 and 5

Then the hypotenuse od this triangle = sqrt [12^2 + 5^2] = sqrt (169) = 13 = (DE)

This is part of the rope length

The other right triangle has legs of 12 and (14 - 5) = 9

The hypotenuse of this triangle is sqrt [ 12^2 + 9^2] = sqrt [225] = 15 = (BE)

This is the other part of the rope

The total length of the rope is (DE) + (BE) = 13 + 15 ≈ 28 ft

CPhill May 31, 2024