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A guy wire runs from the top of a cell tower to a metal stake in the ground. Malika places a 11-foot tall pole to support the guy wire. After placing the pole, Malika measures the distance from the stake to the pole to be 2 ft. She then measures the distance from the pole to the tower to be 35 ft. Find the length of the guy wire, to the nearest foot.

Respuesta :

The guy wire is 111 ft long.

akposevictor

The length of the guy wire, to the nearest foot is: 207 ft.

After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.

  • CD = 11 ft
  • DE = 2 ft
  • BD = 35 ft

Required:

Length of the guy wire (AE)

First, find AB:

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

  • Plug in the values

AB/11 = (35 + 2)/2

AB/11 = 37/2

  • Cross multiply

AB = (37 × 11)/2

AB = 203.5 ft

  • Apply Pythagorean Theorem to find AE:

AE = √(AB² + BE²)

AE = √(203.5² + 37²)

AE = 207 ft (nearest foot)

Therefore, the length of the guy wire, to the nearest foot is: 207 ft.

Learn more about Pythagorean theorem on:

https://brainly.com/question/654982

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