Question

attached to support a telephone pole. Because of surrounding buildings, sidewalks, and roadways, the wire must be anchored exactly 16 feet from the base of the pole. Telephone company workers have only 22 feet of cable, and 1 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?

Answer 1

Using the Pythagorean theorem, it is calculated that the wire can be attached approximately 13.6 feet high from the base of the pole when anchored 16 feet away with a 22-feet cable, considering 1 foot for attachments.

Step-by-step explanation:

To determine how high from the base of the pole the wire can be attached, we can use the Pythagorean theorem, which applies to right-angled triangles. The scenario we're analyzing involves a right-angled triangle where the guy wire represents the hypotenuse, the height at which the wire is attached to the pole represents one leg, and the distance from the pole to where the wire is anchored represents the other leg.

Given that the wire must be anchored exactly 16 feet from the base of the pole and workers have only 22 feet of cable, with 1 foot used for attachments, we have 21 feet for the hypotenuse of the triangle. Let's call the height of attachment h. According to the Pythagorean theorem:

`h^2 + 16^2 = 21^2`

Simplify and solve for h:

`h^2 = 21^2 - 16^2h^2 = 441 - 256h^2 = 185`

The wire can be attached approximately 13.6 feet high from the base of the pole.