Question

O valor de x na figura abaixo é:

Answer 1

Usando a lei dos senos, temos

$\dfrac{100}{sen\;45} = \dfrac{x}{sen\;120}\\\\ \dfrac{100}{ \frac{ \sqrt{2} }{2} } = \dfrac{x}{ \frac{ \sqrt{3}}{2} }\\\\ 100 \frac{ \sqrt{3} }{2} = x \frac{ \sqrt{2} }{2} \\\\ cancelando\;\; 100\;\; com\;\; 2 \;\;e\;\;multiplicando\;\;por\;\;2\\\\ 100 \sqrt{3} = x \sqrt{2} \\\\ x = \dfrac{ 100 \sqrt{3} }{ \sqrt{2} } x = \dfrac{ 100 \sqrt{3} \cdot \sqrt{2}}{ \sqrt{2} \cdot \sqrt{2}} \\\\ x = \dfrac{ 100 \sqrt{6}}{ 2} \\\\ x = 50 \sqrt{6} \approx 122.5$