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 62 feet less than the height of the pole. If the wire is to be 36 feet longer than the height of the pole, what is the height of the pole?

Answer 1

14 feet or 182 feet

Explanation:

Let the height of the pole be x

Distance from the bottom of the pole to the anchor point = (x - 62)

Length of the wire = (36 + x)

From Pythagoras theorem;

(36 + x)2 = + (x - 62) 2

1296 + 72x + x2 = x2 + x2 - 124x + 3844

collecting like terms;

72x + 124x + x2 - 2x2 + 1296 - 3844 = 0

196x - x2 - 2548 = 0

Rearranging the quadratic equation;

x2 - 196x + 2548 =0

(x−14)(x−182)=0

x = 14 feet or 182 feet

Hence, the height of the pole is 14 feet or 182 feet