Question 388566: Find the missing side length that will form an obtuse triangle with sides of length 8 and 10.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Suppose the missing side length is x. A triangle is obtuse if
for some side lengths a, b, c (this is a result from the law of cosines). Therefore,
 -->  , but x must be greater than 2 due to the triangle inequality.
Or, if x is the longest side, then
 -->  . x is less than 18 also because of the triangle inequality. Therefore, any real number in the sets (2, 6), (sqrt(164), 18) will make the triangle obtuse.
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