Question 437478: TriangleABC is an acute triangle. Two of its side measure 11cm and 14cm. What is the rangle of possible values for its third side?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! A corollary from the law of cosines, a triangle with sides a,b,c is acute if and only if  (this inequality is also symmetric, so it applies if you switch the ordering of a,b,c). Hence, for a triangle with sides 11, 14, and x, all three inequalities must be satisfied:
 --> 
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 --> all values x satisfy this inequality.
From the first inequality, the solution set for x is ( ,  ) and from the second inequality, the solution set is ( ,  ). Taking the intersection of these sets, the only possible values for x are those lying in the set (, ).
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