Question

determine o valor de x​

Answer 1

Lei dos Senos: $\frac{a}{SenA}=\frac{b}{SenB}=\frac{c}{SenC}$

 Logo:

$\frac{100}{Sen45^o}=\frac{x}{Sen120^o}\\\\\frac{100}{\frac{\sqrt{2}}{2}}=\frac{x}{Sen60^o}\\\\\frac{100.2}{\sqrt{2}}=\frac{x}{\frac{\sqrt{3}}{2}}\\\\\frac{200}{\sqrt{2}}=\frac{2.x}{\sqrt{3}}\\\\2.\sqrt{2}.x=200.\sqrt{3}\\\sqrt{2}.x=100.\sqrt{3}$

$x=\frac{100.\sqrt{3}}{\sqrt{2}}\\\\x=\frac{100.\sqrt{3}}{\sqrt{2}}.\frac{\sqrt{2}}{\sqrt{2}}\\\\x=\frac{100.\sqrt{6}}{2}\\x=50.\sqrt{6}$

x = 50.√6 m

Dúvidas só perguntar!

Answer 2

$\frac{\sqrt{2} }{2}$

Seno 120° = seno 60° = $\frac{\sqrt{3} }{2}$

O ângulo que falta a medida é 15°

120° + 45° = 165°, 180° - 165° = 15° ( o que falta para inteirar 180° na soma dos ângulos internos do triângulo)

Usando a Lei dos Senos:

$\frac{a}{Sen Â} = \frac{b}{Sen B}=\frac{c}{Sen C}$

x=b

$\frac{100}{Sen45}=\frac{x}{Sen120}$

$\frac{100}{\frac{\sqrt{2} }{2} } =\frac{x}{\frac{\sqrt{3} }{2} }$

$100.\frac{\sqrt{3} }{2}=\frac{\sqrt{2}.x }{2}$

Desconsiderando os denominadores:

100$\sqrt{3}=\sqrt{2}x$

$x=\frac{100\sqrt{3} }{\sqrt{2} }$

Racionalizando:

x=$\frac{100\sqrt{3} }{\sqrt{2} }.\frac{\sqrt{2} }{\sqrt{2} }$

x=$\frac{100\sqrt{6} }{\sqrt{4} }$

x=$\frac{100\sqrt{6} }{2}$

x=50$\sqrt{6} cm$