Question

alguém sabe como faz?? ​

Answer 1

Resposta:

$x=25\sqrt{6}$

Explicação passo-a-passo:

Pela lei dos senos:

$\dfrac{a}{\text{sen}~\hat{\text{A}}}=\dfrac{b}{\text{sen}~\hat{\text{B}}}=\dfrac{c}{\text{sen}~\hat{\text{C}}}$

$\dfrac{x}{\text{sen}~120^{\circ}}=\dfrac{50}{\text{sen}~45^{\circ}}$

$\dfrac{x}{\frac{\sqrt{3}}{2}}=\dfrac{50}{\frac{\sqrt{2}}{2}}$

$\dfrac{x\cdot\sqrt{2}}{2}=\dfrac{50\sqrt{3}}{2}$

$x\cdot\sqrt{2}=50\sqrt{3}$

$x=\dfrac{50\sqrt{3}}{\sqrt{2}}$

$x=\dfrac{50\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$x=\dfrac{50\sqrt{6}}{2}$

$\boxed{x=25\sqrt{6}}$