Question

determine o valor de x no triângulo a seguir​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Pela\,lei\,dos\,senos:}\\\\\rm\dfrac{x}{sen(120^\circ)}=\dfrac{ 100}{sen(45^\circ)}\\\\\rm x\cdot sen(45^\circ)=100\cdot sen(120^\circ)\\\rm x\cdot\dfrac{\sqrt{2}}{\diagup\!\!\!2}=100\cdot\dfrac{\sqrt{3}}{\diagup\!\!\!2}\\\\\rm x\sqrt{2}=100\sqrt{3}\\\rm x=\dfrac{100\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}\\\\\rm x=\dfrac{100\sqrt{6}}{2}\\\\\rm x=50\sqrt{6}\,m\end{array}}$