Mathematics

Question

Need to find line AB
Need to find line AB

1 Answer

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    [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]



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