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A wire is to be attached to support a telephone pole. Because of surrounding buildings, sidewalks, and​ roadways, the wire must be anchored exactly 18 feet from the base of the pole. Telephone company workers have only 25 feet of​ cable, and 22 feet of that must be used to attach the cable to the pole and to the stake on the ground. How high from the base of the pole can the wire be​ attached?

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Luv2Teach
This situation is a right triangle with the base measuring 18 and the hypotenuse 22.  We are looking for x, the height up the pole that the wire is going to be attached to.  We will use Pythagorean's Theorem to find the missing length.  [tex]22^2-18^2=x^2[/tex]  and  [tex]484-324=x^2[/tex].  x^2 = 160 so x = [tex]4 \sqrt{10} [/tex] or 12.65 feet
MrRoyal

The support wire is an illustration of Pythagoras theorem

The wire should be placed at 12.65 feet from the pole

The usable length of the wire is given as:

[tex]\mathbf{l = 22}[/tex]

The wire must be anchored at 18 ft.

So, the height is:

[tex]\mathbf{h = 18}[/tex]

The distance (d) from the height of the pole to the ground is illustrated using the following Pythagoras theorem

[tex]\mathbf{l^2 = h^2 + d^2}[/tex]

Substitute known values

[tex]\mathbf{22^2 = 18^2 + d^2}[/tex]

[tex]\mathbf{484 = 324 + d^2}[/tex]

Subtract 324 from both sides

[tex]\mathbf{484 - 324 = d^2}[/tex]

[tex]\mathbf{160 = d^2}[/tex]

Take square roots of both sides

[tex]\mathbf{12.65 = d}[/tex]

Rewrite as:

[tex]\mathbf{d = 12.65 }[/tex]

Hence, the wire should be placed at 12.65 feet from the pole

Read more about Pythagoras theorem at:

https://brainly.com/question/15138986