Question

Calcule o valor de a ​

Answer 1

$\displaystyle \underline{\text{Lei dos senos}}: \\\\ \frac{\text{AB}}{\text{sen}(45^\circ)}=\frac{\text{AC}}{\text{sen}(60)^{\circ}} \\\\\\ \underline{\text{substituindo os respectivos valores}}: \\\\ \frac{6}{\displaystyle \frac{\sqrt 3}{2}}=\frac{\displaystyle \text a}{\displaystyle \frac{\sqrt{2}}{2}}\\\\\\ \text a = \frac{6\sqrt{2}}{\sqrt{3}} \\\\\\ \text a = \frac{6\sqrt{2}.\sqrt{3}}{\sqrt{3}\sqrt{3}} \\\\\\ \text a = \frac{6\sqrt{6}}{3} \\\\ \huge\boxed{\text a = 2\sqrt{6}\ \text{cm} \ }\checkmark$