Question

A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 41 feet less than the height of the pole. If the wire is to be 9 feet longer than the height of the pole, what is the height of the pole?

Answer 1

80 feet

Explanation:

Let x represent the height of the pole.

We have been given that a telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 41 feet less than the height of the pole. So the distance between bottom of pole to the anchor point would be
`x-41`.

The wire is to be 9 feet longer than the height of the pole, so length of the wire would be
`x+9`.

We know that length of the wire would be hypotenuse of right triangle, so we can use Pythagoras theorem as:

`(x+9)^2=x^2+(x-41)^2`

`x^2+18x+81=x^2+x^2-82x+1681`

`x^2+18x+81=2x^2-82x+1681`

`2x^2-82x+1681=x^2+18x+81`

`2x^2-x^2-82x-18x+1681-81=0`

`x^2-100x+1600=0`

`x^2-20x-80x+1600=0`

`x(x-20)-80(x-20)=0`

`(x-20)(x-80)=0`

`(x-20)=0,(x-80)=0`

`x=20,x=80`

Since the distance from the bottom of the pole to the anchor point is 41 feet less than the height of the pole, so 20 feet cannot be height of the pole.

Therefore, the height of the pole is 80 feet.