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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• 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