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for c:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ c^2=4^2+5^2-2(4)(5)\cos 100 \\ c^2=16+25-40\cos 100 \\ c^2=41-40\cos 100 \\ c^2=47.945 \\ c=\sqrt[]{47.945} \\ c=6.92 \end{gathered}[/tex]for A:
[tex]\begin{gathered} \frac{c}{\sin C}=\frac{a}{\sin A} \\ \sin A=\frac{a\times\sin C}{c} \\ \sin A=\frac{4\times\sin 100}{6.92} \\ A=\sin ^{-1}\frac{4\times\sin 100}{6.92} \\ A=34.7 \end{gathered}[/tex]for B:
[tex]180-100-34.7=45.3[/tex]answer: D