Question

Ajuda aí

Estou com uma avaliação de matemática e não estou conseguindo resolver!

Answer 1

Resposta:

Explicação passo-a-passo:

Basta usar a Lei dos Senos

a)

$\dfrac{x}{sen45}=\dfrac{\sqrt{6}}{sen60}\\\\\\\dfrac{x}{\dfrac{\sqrt{2}}{2} }=\dfrac{\sqrt{6}}{\dfrac{\sqrt{3}}{2}}\\\\\\\dfrac{x}{\sqrt{2}}=\dfrac{\sqrt{6}}{\sqrt{3}}\\\\\\\dfrac{x}{\sqrt{2}}=\sqrt{\dfrac{6}{3}}\\\\\\\dfrac{x}{\sqrt{2}}=\sqrt{2}\\\\x=\sqrt{2}.\sqrt{2}\\\\\\x=2$

b)

Neste item devemos inicialmente encontrar o valor do ângulo oposto ao x.

β=180-75-45=180-120=60

$\dfrac{x}{sen60}=\dfrac{2\sqrt{3}}{sen45}\\\\\\\dfrac{x}{\dfrac{\sqrt{3}}{2}}=\dfrac{2\sqrt{3}}{\dfrac{\sqrt{2}}{2}}\\\\\\\dfrac{x}{\sqrt{3}}=\dfrac{2\sqrt{3}}{\sqrt{2}}\\\\\\\\x=\dfrac{2\sqrt{3}.\sqrt{3}}{\sqrt{2}}\\\\\\x=\dfrac{2.3}{\sqrt{2}}\\\\\\x=\dfrac{6}{\sqrt{2}}\\\\Racionalizando\\\\x=\dfrac{6\sqrt{2}}{\sqrt{2}\sqrt{2}}\\\\\\x=\dfrac{6\sqrt{2}}{2}\\\\\\x=3\sqrt{2}$