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A 200-foot long support wire attaches to a cell phone tower at a height of 50 feet from the ground. To the nearest tenth of a foot, what is the distance along the ground from the center of the tower to the point where the wire touches the ground? 193.6 ft 21.2 ft 7.1 ft 206.2 ft

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Your answer is 193.6, my dear.
User AMiGo
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Answer: 193.6 ft

Explanation:

Since, the length of the wire = 200 ft,

And, the height of the tower = 50 ft,

Let x be the distance along the ground from the center of the tower to the point where the wire touches the ground,

By the below diagram,


(\text{The length of the wire})^2 = (\text{The height of the tower})^2 +x^2


\implies 200^2=50^2+x^2


\implies -x^2 = 2500-40000=-37500


\implies x^2=37500\implies x = 193.64916731\approx 193.6

Hence, the distance along the ground from the center of the tower to the point where the wire touches the ground is approximately 193.6 feet.

A 200-foot long support wire attaches to a cell phone tower at a height of 50 feet-example-1
User Anyweez
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