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Train tracks are made of metal. Consequently, they expand when it's warm and shrink when it's cold. When riding in a train, you hear the clickety-clack of the wheels going over small gaps left in the tracks to allow for this expansion. Suppose you were a beginner at laying railroad tracks and forgot to put in the gaps. Instead, you made a track 01 mile long that was firmly fixed at each end. On a hot day, suppose the track expanded by A = 8 feet and therefore buckled up in the middle, creating a triangle.

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michell96

The height of the triangle that forms the train track is 145,38 ft

How to calculate the height of the triangle?

To calculate the height of the triangle we must take into account the information provided by

  • Base of the triangle = 1 mile = 5280 feet
  • Railroad track expansion = 8 feet

According to the above, we must perform the following operations:

  • 5280 ÷ 2 = 2640
  • 8 ÷ 2 = 4
  • 2640 + 4 = 2644

Subsequently, we must apply the Pythagorean theorem to find the height of the triangle having 2 data:

  • Base: 2640ft
  • Hypotenuse: 2644 ft

  • 2644² = x² + 2640²
  • x² = 2644² - 2640²
  • x = [tex]\sqrt[2]{2644^{2} + 2640^{2}}[/tex].
  • x = [tex]\sqrt[2]{21137}[/tex]
  • x = 145,38 ft

That makes x approximately 145,38 ft.

Learn more about triangles in: https://brainly.com/question/2269348

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