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 49 feet less than the height of the pole. If the wire is to be 14 feet longer than the height of the pole, what is the height of the pole?

Answer 1

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Answer:

105 ft

Explanation:

Let x represent the height of the pole. Then (x -49) is the distance from the pole to the anchor point, and (x+14) is the length of the wire from the top of the pole to the anchor point.

The Pythagorean theorem gives us the relation ...

(x +14)² = x² +(x -49)²

x² +28x +196 = x² +x² -98x +2401 . . . . eliminate parentheses

x² -126x +2205 = 0 . . . . . . . . put in standard form

x² -126x +3969 -1764 = 0 . . . . "complete the square)

(x -63) = ±√1764 . . . . . . add 1764, take the square root

x = 63 +42 = 105 . . . . . . highest value root. The pole must be higher than 49 feet

The height of the pole is 105 feet.