Question

You are given 90 feet of guy wire for a pole 60 feet tall and you had to attach the wire to the top of the pole. How far away from the base of the pole could you anchor the guy wire without having to cut off any excess wire?

Answer 1

The connection of the wire to the top of the pole and the distance of the wire from the base of the pole will form a right-angled triangle.

The wire will be at approximately 67.08 feet from the base of the pole.

Given that:

$Length = 90ft$

$Height = 60ft$

The distance away from the base of the pole will be calculated using Pythagoras theorem as follows:

$Length^2 = Height^2 + Base^2$

So, we have:

$90^2 = 60^2 + Base^2$

$8100 = 3600 + Base^2$

Collect like terms

$Base^2 = 8100 - 3600$

$Base^2 = 4500$

Take square roots of both sides

$Base = 67.08$

Hence, the wire will be at approximately 67.08 feet from the base of the pole.

Read more about Pythagoras theorem at:

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Answer 2

The guy wire should be anchored at 67.082 feets from the pole.

Length of wire = 90 feets

Height of pole = 60 feets

Let the Distance of anchor from pole = d

Using Pythagoras:

Hypotenus² = adjacent² + opposite²

Length of wire = hypotenus

adjacent² = Hypotenus² - opposite²

d² = 90² - 60²

d² = 8100 - 3600

d² = 4500

d = √4500

d = 67.082 feets

The guy wire should be anchored at 67.082 feets from the pole.

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