Question

Observe o triângulo ABC abaixo e determine a medida do lado AC:
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Answer 1

Explicação passo-a-passo:

Pela lei dos senos:

$\sf \dfrac{x}{sen~60^{\circ}}=\dfrac{3\sqrt{2}}{sen~45^{\circ}}$

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

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

$\sf \dfrac{x\sqrt{2}}{2}=\dfrac{3\sqrt{6}}{2}$

$\sf x\sqrt{2}=3\sqrt{6}$

$\sf x=\dfrac{3\sqrt{6}}{\sqrt{2}}$

$\sf x=\dfrac{3\sqrt{6}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

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

$\sf x=\dfrac{3\cdot2\sqrt{3}}{2}$

$\sf x=\dfrac{6\sqrt{3}}{2}$

$\sf \red{x=3\sqrt{3}}$