Find \(BC\).
https://latex.artofproblemsolving.com/f/e/4/fe45662f573f87e30f9f30d0b1ef1f94b4c22fc2.png
+9466 
By the Law of Cosines:
\(a^2 = c^2 + b^2 - 2cb \cos A\\~\\ (\overline{\text{BC}})^2 \,=\,(7\sqrt2)^2+(6)^2-2(7\sqrt2)(6)\cos(45°)\\~\\ (\overline{\text{BC}})^2 \,=\,98+36-(84\sqrt2)(\frac{\sqrt2}{2})\\~\\ (\overline{\text{BC}})^2 \,=\,98+36-84\\~\\ (\overline{\text{BC}})^2 \,=\,50\\~\\ \overline{\text{BC}} \,=\,\sqrt{50}\\~\\ \overline{\text{BC}} \,=\,5\sqrt{2}\)
+9466
By the Law of Cosines:
\(a^2 = c^2 + b^2 - 2cb \cos A\\~\\ (\overline{\text{BC}})^2 \,=\,(7\sqrt2)^2+(6)^2-2(7\sqrt2)(6)\cos(45°)\\~\\ (\overline{\text{BC}})^2 \,=\,98+36-(84\sqrt2)(\frac{\sqrt2}{2})\\~\\ (\overline{\text{BC}})^2 \,=\,98+36-84\\~\\ (\overline{\text{BC}})^2 \,=\,50\\~\\ \overline{\text{BC}} \,=\,\sqrt{50}\\~\\ \overline{\text{BC}} \,=\,5\sqrt{2}\)
