Question

Me ajudem a questão está na foto ​

Answer 1

Lei dos cossenos :

$\text a^2 =\text b^2+\text c^2-2\text{b.c}.\text{cos}(150^\circ)$

Sabemos que :

$\text{cos}(150^\circ)=\text{cos}(180^\circ-30^\circ) = -\text{cos}(30^\circ)$

Substituindo :

$\text a^2 =\text b^2+\text c^2-2\text{b.c}.(-\text{cos}(30^\circ)) \\\\\ \text a^2 =\text b^2+\text c^2+2\text{b.c}.\text{cos}(30^\circ)$

Substituindo os respectivos valores :

$\displaystyle \text a^2 = (4\sqrt{3})^2+6^2+2.6.4\sqrt{3}.\frac{\sqrt{3}}{2} \\\\\ \text a^2=16.3+36+24.3 \\\\ \text a^2=48+36+72 \\\\ \text a^2 = 156 \\\\ \text a = \sqrt{4.39} \\\\\ \huge\boxed{\text a =2\sqrt{39}\ }\checkmark$

letra d