Question

Determine o valor de x em cada caso: A=x,B=2√3,C=2√7 e Cosseno de 30°​

Answer 1

Pela Lei dos Cossenos temos:

    $x^{2}=(2\sqrt{3})^{2}+(2\sqrt{7})^{2}-2*(2\sqrt{3})*(2\sqrt{7})*cos(30^{o})$ ⇔

⇔ $x^{2}=(4*3)+(4*7)-8\sqrt{3}\sqrt{7}*\frac{\sqrt{3}}{2}$ ⇔

⇔ $x^{2}=12+28-\frac{8\sqrt{3}\sqrt{7}\sqrt{3}}{2}$ ⇔

⇔ $x^{2}=40-4(\sqrt{3})^{2}\sqrt{7}$ ⇔

⇔ $x^{2}=40-4*3\sqrt{7}$ ⇔

⇔ $x^{2}=40-12\sqrt{7}$ ⇔

⇔ $x=-\sqrt{40-12\sqrt{7}}$  ∨  $x=\sqrt{40-12\sqrt{7}}$ ⇔

⇔ $x=-\sqrt{(2^{2}*10)-(2^{2}*3\sqrt{7})}$  ∨  $x=\sqrt{(2^{2}*10)-(2^{2}*3\sqrt{7})}$ ⇔

⇔ $x=-\sqrt{2^{2}(10-3\sqrt{7})}$  ∨  $x=\sqrt{2^{2}(10-3\sqrt{7})}$ ⇔

⇔ $x=-\sqrt{2^{2}}*\sqrt{(10-3\sqrt{7})}$  ∨  $x=\sqrt{2^{2}}*\sqrt{(10-3\sqrt{7})}$ ⇔

⇔ $x=-2\sqrt{10-3\sqrt{7}}$  ∨  $x=2\sqrt{10-3\sqrt{7}}$ ⇔

⇔ $x=2\sqrt{10-3\sqrt{7}}$    pois x é uma medida de comprimento