$\"\"$

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The length of b = 13, hypotenuse c = $\"\"$ , and length a = ?.

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Apply pythagorean theorem: $\"\"$ .

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$\"\"$ (Substitute b = 13, and c = $\"\"$ )

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Evaluate powers: $\"\"$ .

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$\"\"$

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Apply subtraction property of equality: a = b then $\"\"$ .

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$\"\"$ (Subtract 169 from each side) $\"\"$

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Apply commutative property of addition: a + b = b + a.

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$\"\"$

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Subtract: $\"\"$ )

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Apply square roots property: $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$ (Evaluate power: $\"\"$ )

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The positive value of a = 8. $\"\"$

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The length of $\"\"$ .