Question

Now given a rope hanging from the top of a pole. The end lying on the ground is 3 chi long. When tightly stretchedit is 8 chi from the bottom of the pole. Let x represent the height of the pole. Tell: how long is the rope and how high is the pole

Answer 1

Height of the pole = 9.17 chi.

Length of the rope = 12.17 chi.

Explanation:

Given that the rope is hanging from the top of a pole having height x chi and the portion of the rope lying on the ground is 3 chi.

So, the length of the rope= x + 3 chi.

Let AB represents the pole in the figure, and one end of the rope is at point A.

When the rope is tightly stretched, let C be the other end of the rope as shown in the triangle.

The length of the rope = AC.

\Rightarrow AC=x+3 chi.

Distance from the bottom of the pole, point A, to the other end of the pole, point B, is 8 chi.

So, BC=8 chi.

As the triangle ABC is a right-angled triangle, so by using Pythagoras theorem,

`AC^2= AB^2+BC^2`

`\Rightarrow (x+3)^2=x^2+8^2`

`\Rightarrow x^2+6x+9=x^2+64`

`\Rightarrow 6x=64-9=55`

`\Rightarrow x=55/6=9.17` chi.

Hence, the height of the pole,
`AB=x=9.17` chi,

and the length of the rope,
`x+3=9.17+3=12.17` chi.