SOLUTION: TriangleABC is an acute triangle. Two of its side measure 11cm and 14cm. What is the rangle of possible values for its third side?
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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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