Question

O valor de X na figura abaixo é:

Answer 1

$\tan{30} = \frac{x}{8\sqrt{3} + \overline{BC}} \Rightarrow 8\sqrt{3} + \overline{BC} = \frac{x}{\tan{30}} \Rightarrow \overline{BC} = \frac{x}{\tan{30}} - 8\sqrt{3} \\ \\ \tan{60} = \frac{x}{\overline{BC}} \Rightarrow \overline{BC} = \frac{x}{\tan{60}} \\ \\ Igualando \: as \: express\~{o}es: \\ \\ \frac{x}{\tan{30}} - 8\sqrt{3} = \frac{x}{\tan{60}} \\ \\ \frac{x}{\frac{\sqrt{3}}{3}} - 8\sqrt{3} = \frac{x}{\sqrt{3}} \\ \\ \frac{3x}{\sqrt{3}} - 8\sqrt{3} = \frac{x}{\sqrt{3}} \qquad \times(\sqrt{3})$

$3x - 8 \cdot 3 = x \\ 3x - 24 = x \\ 3x - x = 24 \\ 2x = 24 \\ x = \frac{24}{2} \\ \\ \boxed{x = 12}$