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Determine the range of possible side lengths of the third side AB of ABC from least to greatest

User Mattsh
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To determine the range of possible side lengths of the third side AB of ABC, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Therefore, we have:

AC + BC > AB
10 + 7 > AB
17 > AB

AB + AC > BC
AB + 10 > 7
AB > -3

AB + BC > AC
AB + 7 > 10
AB > 3

Therefore, the range of possible side lengths for AB is 3 < AB < 17.
User Ali Khosro
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