Question

Resolva com a lei dos senos.

Answer 1

Resposta:

$\sf \dfrac{x}{\sin{45^\circ}} = \dfrac{4}{\sin{60^\circ}}$

$\sf \sin{60^\circ} x = 4 \sin{45^\circ}$

$\sf \dfrac{\sqrt{3} }{2} \cdot x = 4\cdot \dfrac{\sqrt{2} }{2} \quad \gets \mbox{ \sf Cancela o denominador 2}$

$\sf \sqrt{3} \cdot x = 4\cdot \sqrt{2}$

$\sf x = \dfrac{4\cdot \sqrt{2} }{\sqrt{3} } \quad \gets \mbox{ \sf Racionalizar o denominador}$

$\sf x = \dfrac{4\cdot \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} }$

$\sf x = \dfrac{4\cdot \sqrt{2}\cdot \sqrt{3} }{\sqrt{3^2} }$

$\sf x = \dfrac{4\cdot \sqrt{2 \times 3} }{3 }$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x = \dfrac{4\; \sqrt{6} }{3 } }}} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo: