Example 5: In the late 1800’s, settlers created tents by throwing a piece of cloth thrown over two poles secured to the ground with stakes. The cloth tent formed an isosceles triangle. The cloth was 10 meters by 10 meters; the base of the tent (measured from stake to stake) was 6 meters wide.  How long were the tent poles? (The poles are perpendicular to the ground.)

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  Draw a picture

  
  
  
• The height of the pole, one leg of the right triangle,  is ___?____.
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  x
  
• The length of the hypotenuse of the right triangle is _____?_____.
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  5 m
  
• The pole is the perpendicular midpoint of the ____?____ of the triangle.
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  base
  
• The length of the other leg of the right triangle is ____?_____.
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  6/2 = 3
  
• The Pythagorean Theorem is ______?______
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  a² + b² = c²
  
• Substitute the values for a, b, and c: ______?______
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  3² + x² = 5²
  
• Square the numerical values: ______?_______
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  9 + x² = 25
  
• Solve for x²: _____?_____
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  9 - 9 + x² = 25 - 9 ⇒ x² = 16
  
• Take the square root of both sides. ____?_____
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  √x² = √16
  
• Simplify both radicals. _____?______
  ***NOTE: Since the radicals represent lengths only the positive value is used.
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  x = 4

• The pole is ___?___ meters long.
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  Check Your Answer

  4