Question

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

Answer 1

Your answer is 193.6, my dear.

Answer 2

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.