[tex]\displaystyle\\
\text{We apply the generalized Pythagorean Theorem:}\\\\
a^2=b^2+c^2-2bc\cdot \cos A\\\\
AB^2=AC^2+BC^2-2\cdot AC\cdot BC\cdot\cos\widehat{ACB}\\\\
AB^2=620^2+455^2-2\cdot620\cdot455\cdot\cos(150^o)\\\\
AB^2 = 384400+207025-2\cdot282100\cdot\cos(180-30)\\\\
AB^2=384400+207025-2\cdot282100\cdot(-\cos(30))\\\\
AB^2=384400+207025+2\cdot282100\cdot\cos(30)\\\\
AB^2=384400+207025+2\cdot282100\cdot\frac{ \sqrt{3} }{2}\\\\
AB^2=384400+207025+282100\cdot\sqrt{3} [/tex]
[tex]AB^2=384400+207025+282100\cdot\sqrt{3} \\\\
AB^2=384400+207025+282100\cdot 1,73 \\\\
AB^2=384400+207025+488033 \\\\
AB^2=1079458 \\\\
AB = \sqrt{1079458} =1038,96968 \approx \boxed{1039 ~\texttt{yards}}[/tex]
