document.write( "Question 530511: Can we make a triangle with side lengths: 12, 18, and 16? \n" ); document.write( "

Algebra.Com's Answer #350178 by oberobic(2304) $\"\"$ $\"About$

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Applying the law of cosines:
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\n" ); document.write( "c^2 = a^2 + b^2 - 2*a*b*(cos(x)), where 'x' is the angle between 'a' and 'b'.
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\n" ); document.write( "c^2 - a^2 - b^2 = -2*a*b*(cos(x))
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\n" ); document.write( "(c^2 -a^2 -b^2)/(-2*a*b) = cos(x)
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\n" ); document.write( "(18^2 -12^2 -16^2)/(-2*12*16) = .1979166666666667
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\n" ); document.write( "We can see that .1979166666666667 is a valid value for the cosine function.
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\n" ); document.write( "So, yes, you could have a triangle with sides of 12, 16, and 18.
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\n" ); document.write( "Done.
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