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vaieri [72.5K]
2 years ago
11

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.
Mathematics
1 answer:
Nadya [2.5K]2 years ago
4 0

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

<h3>How to calculate the height of the triangle?</h3>

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 = \sqrt[2]{2644^{2} + 2640^{2}}.
  • x = \sqrt[2]{21137}
  • x = 145,38 ft

That makes x approximately 145,38 ft.

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

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