Question

determine o valor de x na figura :

Answer 1

Explicação passo-a-passo:

Pela lei dos senos:

$\sf \dfrac{x}{sen~120^{\circ}}=\dfrac{100}{sen~45^{\circ}}$

$\sf \dfrac{x}{\frac{\sqrt{3}}{2}}=\dfrac{100}{\frac{\sqrt{2}}{2}}$

$\sf \dfrac{x\cdot\sqrt{2}}{2}=\dfrac{100\sqrt{3}}{2}$

$\sf x\sqrt{2}=100\sqrt{3}$

$\sf x=\dfrac{100\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf x=\dfrac{100\sqrt{6}}{2}$

$\sf x=50\sqrt{6}~m$