Question

Gente alguém me ajuda a resolver essa questão?

o gabarito dela é FG = 163m e EF = 223m

Answer 1

Lei dos Senos

$\frac{200}{sin(60)} = \frac{FG}{sin(45)}\\\\\frac{200}{\frac{\sqrt{3}}{2} } =\frac{FG}{\frac{\sqrt{2} }{2} } \\\\\frac{200\sqrt{6} }{3} = FG$

$\frac{200}{\sqrt{3}}{2}} =\frac{EF}{sin(75)}$

sin(75) = sin(45 +30) = (sin(45) * cos(30)) + (cos(45) * sin(30))

$(\frac{\sqrt{2}}{2} *\frac{\sqrt{3} }{2} )+(\frac{\sqrt{2} }{2} * \frac{1}{2} )\\\\\frac{\sqrt{6} +\sqrt{2} }{4}$

$\frac{200}{\frac{\sqrt{3} }{2} } =\frac{EF}{(\frac{\sqrt{6} +\sqrt{2}}{4} )}\\\\\frac{200\sqrt{3} }{3} =\frac{2(EF)}{(\sqrt{6} +\sqrt{2})}\\\\\frac{100\sqrt{3}(\sqrt{6} +\sqrt{2} )}{3} = EF\\\\\frac{100(\sqrt{18} +\sqrt{6})}{3} = EF\\\\\frac{100(3\sqrt{2} +\sqrt{6} }{3} = EF\\ \\\frac{300\sqrt{2} +100\sqrt{6} }{3} = EF$