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 23 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

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Answer:

56 feet

Explanation:

Let x represent the height of the pole. Then the distance to the anchor point is (x-23), and the length of the wire is (x+9). The Pythagorean theorem tells you the relation between these values is ...

(x+9)² = x² +(x -23)²

0 = x² -64x +448 . . . . . subtract the left side, put in standard form

0 = (x -8)(x -56) . . . . . . factor

The solutions to the quadratic are x=8 and x=56. For our purposes, we require x > 23 so the distances are positive. That means x=56 is the solution of interest.

The pole is 56 feet tall.