Question

Observe a figura abaixo e determine o comprimento de AC?

Answer 1

Explicação passo-a-passo:

Seja AC = x

Pela lei dos senos:

$\sf \dfrac{x}{sen~60^{\circ}}=\dfrac{12}{sen~45^{\circ}}$

$\sf \dfrac{x}{\frac{\sqrt{3}}{2}}=\dfrac{12}{\frac{\sqrt{2}}{2}}$

$\sf \dfrac{x\sqrt{2}}{\not{2}}=\dfrac{12\sqrt{3}}{\not{2}}$

$\sf x\sqrt{2}=12\sqrt{3}$

$\sf x=\dfrac{12\sqrt{3}}{\sqrt{2}}$

$\sf x=\dfrac{12\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf x=\dfrac{12\sqrt{6}}{2}$

$\sf x=6\sqrt{6}~cm$

Letra E