Answer
The value of $ c $ to the nearest tenth is $6.2$.
Work Step by Step
Using the Law of Cosines, we get, ${{c}^{2}}={{a}^{2}}+{{b}^{2}}-2ab\cos C $
Substitute the values $ C=68{}^\circ,a=5,b=6$ ;
So, $\begin{align}
& {{c}^{2}}={{a}^{2}}+{{b}^{2}}-2ab\cos C \\
& {{c}^{2}}={{5}^{2}}+{{6}^{2}}-2\left( 5 \right)\left( 6 \right)\cos 68{}^\circ \\
& =61-60\cos 68{}^\circ \\
& =38.52
\end{align}$
Further, $\begin{align}
& c=\sqrt{38.52} \\
& \approx 6.2
\end{align}$
So, the value of $ c $ is $6.2$.
Therefore, the value of $ c $ to the nearest tenth is $6.2$.
