Use the law of cosines: [tex] c^2=a^2+b^2-2ab\cos C [/tex]
We have:
[tex]c=x\\a=3in\\b=7in\\C=54^o[/tex]
substitute:
[tex]\cos54^o\approx0.5878\\\\c^2=3^2+7^2-2\cdot3\cdot7\cdot0.5878\\\\c^2=9+49-24.6876\\\\c^2=33.3129\to c=\sqrt{33.3129}\\\\c\approx5.8[/tex]
