Question

Alguém pode ajudar????

Answer 1

Lei dos cossenos:

$\boxed{\boxed{a^{2}=b^{2}+c^{2}-2\cdot b\cdot c\cdot cos~\^A}}$

Onde  é o ângulo oposto ao lado 'a'
____________________

No exercício:

$a^{2}=(6\sqrt{2})^{2}+10^{2}-2\cdot6\sqrt{2}\cdot10\cdot cos~45\º\\\\a^{2}=6^{2}(\sqrt{2})^{2}+100-120\sqrt{2}\cdot\frac{\sqrt{2}}{2}\\\\a^{2}=36\cdot2+100-60\sqrt{2}\cdot\sqrt{2}\\\\a^{2}=72+100-60\cdot2\\\\a^{2}=172-120\\\\a^{2}=52\\\\a=\sqrt{52}\\\\a=\sqrt{4\cdot13}\\\\a=\sqrt{4}\cdot\sqrt{13}\\\\\\\boxed{\boxed{a=2\sqrt{13}~cm}}$