Question

Urgente pfv, preciso do valor de x​

Answer 1

Resposta:

Aplicar a lei do seno:

$\sf \dfrac{x}{\sin {60^\circ}} = \dfrac{8 \; cm}{\sin {\alpha}}$

$\sf \dfrac{x}{\dfrac{\sqrt{3} }{2} } = \dfrac{8 \; cm}{\sin {45^\circ}}$

$\sf \dfrac{2x}{\sqrt{3} } = \dfrac{8 \; cm}{\dfrac{\sqrt{2} }{2} }$

$\sf \dfrac{2x}{\sqrt{3} } = \dfrac{16 \; cm}{\sqrt{2} }$

$\sf 2\,\sqrt{2} \; x = 16\, \sqrt{3} \; cm$

$\sf x = \dfrac{16\, \sqrt{3}\; cm }{2\, \sqrt{2} }$

$\sf x = \dfrac{8\, \sqrt{3}\; cm }{ \sqrt{2} } \times \dfrac{\sqrt{2} }{\sqrt{2} }$

$\sf x = \dfrac{8\, \sqrt{6}\; cm }{ \sqrt{4} }$

$\sf x = \dfrac{8\, \sqrt{6}\; cm }{ 2}$

$\framebox{ \boldsymbol{ \sf \displaystyle \sf x = 4\, \sqrt{6} \; cm } }} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo:

$\sf \hat{\alpha} = 45^\circ \iff 180^\circ -( 75^\circ + 60^\circ)$

A lei dos senos: