Question

questão 15, não estou conseguindo achar o valor

Answer 1

$\hat{A}=45^{\circ}$

$\hat{B}=30^{\circ}$

$\boxed{a+b=\sqrt{2}+1}$

$\boxed{\dfrac{a}{\sin{\hat{A}}}=\dfrac{b}{\sin{\hat{B}}}=\dfrac{c}{\sin{\hat{C}}}}\ \text{(Lei dos Senos de Al-Tusi)}$

$\dfrac{a}{\sin{45^{\circ}}}=\dfrac{b}{\sin{30^{\circ}}}\Longrightarrow\dfrac{a}{\bigg(\frac{\sqrt{2}}{2}\bigg)}=\dfrac{b}{\bigg(\frac{1}{2}\bigg)}\ \therefore\ \boxed{a=b\sqrt{2}}$

$b\sqrt{2}+b=\sqrt{2}+1\Longrightarrow b(\sqrt{2}+1)=\sqrt{2}+1\ \therefore\ \boxed{b=1}$

$a=\sqrt{2}+1-b\Longrightarrow a=\sqrt{2}+1-1\ \therefore\ \boxed{a=\sqrt{2}}$