Answer :
Since interior angles of any triangle add up to 180, we have
[tex]\angle B+60+44=180[/tex]which gives
[tex]\begin{gathered} \angle B+104=180 \\ \text{then} \\ \angle B=180-104 \\ \angle B=76 \end{gathered}[/tex]Now, in order to find c, we can apply the law of sines, that is,
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin B}{b} \\ \text{that is,} \\ \frac{\sin60}{c}=\frac{\sin76}{7} \end{gathered}[/tex]or equivalently,
[tex]\frac{c}{\sin60}=\frac{7}{\sin 76}[/tex]Then, by moving sin60 to the right hand side, we get
[tex]c=\sin 60\times\frac{7}{\sin 76}[/tex]which gives
[tex]\begin{gathered} c=0.8660\times\frac{7}{0.97029} \\ c=6.24757 \end{gathered}[/tex]Similarly, by the law of sines, we have
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \text{that is,} \\ \frac{\sin 44}{a}=\frac{\sin 76}{7} \end{gathered}[/tex]or equivalently,
[tex]\frac{a}{\sin44}=\frac{7}{\sin 76}[/tex]then, a is given as
[tex]\begin{gathered} a=\sin 44\times\frac{7}{\sin 76} \\ a=0.6946\times\frac{7}{0.97029} \\ a=5.011 \end{gathered}[/tex]In summary, the answers are
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