Answer
$179\ km$
Work Step by Step
Given $C=118^\circ, a=75.0\ km, b=131\ km$, use the Law of Cosines, we have
$c^2=a^2+b^2-2ab\ cosC=(75.0)^2+(131)^2-2(75.0)(131)cos118^\circ\approx32011$. Thus $c=\sqrt {32011}\approx179\ km$
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