Algebra Logical Pythagorean theorem helpA wire is attached to the top of a pole. The pole is 2 feet shorter than the wire, and the distance from the wire on the ground to the bottom of the pole is 9 feet less than the length of the wire. Find the length of the wire and the height of the pole.Hint: Use the pythagorean theorem then set up a quadratic equation equal to zero and solve. I got c=17 and c=5 but I don't know what the length of the wire is or the height of the pole.

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Algebra Logical Pythagorean theorem helpA wire is attached to the top of a pole. The pole is 2 feet shorter than the wire, and the distance from the wire on the ground to the bottom of the pole is 9 feet less than the length of the wire. Find the length of the wire and the height of the pole.Hint: Use the pythagorean theorem then set up a quadratic equation equal to zero and solve. I got c=17 and c=5 but I don&#039;t know what the length of the wire is or the height of the pole.

Immanuel Glenn · Accepted Answer

Your work is correct. To complete the problem, you must consider what each answer implies about the lengths of the legs of the triangle.Since the pole is 2 feet shorter than the wire, it has length c−2 ft.Since the distance from the wire on the ground to the bottom of the pole is 9 feet less than the length of the wire, the base of the right triangle has length c−9 ft. Hence, by the Pythagorean Theorem,                    (        c        −        2                 ft.                  )          2                +        (        c        −        9                 ft.                  )          2                                    =                  c          2                                              c          2                −        4        c                 ft.        +        4                           ft.          2                +                  c          2                −        18        c                 ft.        +        81                           ft.          2                                    =                  c          2                                              c          2                −        22        c                 ft.        +        85                           ft.          2                                    =        0                            (        c        −        5                 ft.        )        (        c        −        17                 ft.        )                            =        0            Hence, c=5 ft. and c=17 ft. satisfy the equation. However, if c=5 ft., then the distance from the point where the wire touches the ground to the base of the pole is c−9 ft.=−4 ft., which is impossible since a distance cannot be negative. Hence, c=17 ft., so the height of the pole is c−2 ft.=15 ft.

Algebra Logical Pythagorean theorem help A wire is attached to the top of a pole. The pole is 2 fee

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