16, Có \(cosa>0\Rightarrow0< a< 90\)
\(cosa=\dfrac{1}{3}\Rightarrow a\approx649,5\Rightarrow sin\left(649,5\right)\approx\dfrac{-2\sqrt{2}}{3}\)
17, \(cosa< 0\Rightarrow90^o< a< 180\\ sin\left(135\right)=sin\left(180-135\right)=sin45=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow sin\left(45\right)< sina\Leftrightarrow sin\left(135\right)< sina\Rightarrow D\)
18, \(c^2=a^2+b^2-2abcosC\\ \Rightarrow c=\sqrt{\sqrt{2}^2+\sqrt{3}^2-2.\sqrt{2}\sqrt{3}cos30}=\left(C\right)\)
\(19,2bccosA=b^2+c^2-a^2\\ \Rightarrow cosA=\dfrac{5^2+8^2-7^2}{2.5.8}=\dfrac{1}{2}\Rightarrow A=60^o\)
\(20,B=180-30-75=75^o\\ \dfrac{b}{sinB}=\dfrac{c}{sinC}\Leftrightarrow\dfrac{4}{sin\left(75\right)}=\dfrac{c}{sin75}\Rightarrow c=AB=4\\ \Rightarrow S_{ABC}=\dfrac{1}{2}bcsinA=8\\ 21,\dfrac{8\left(c\right)}{sinC}=\dfrac{4\sqrt{6}}{sin60}\Rightarrow C=45^o\\ 22,cos\left(A+B\right)=\dfrac{-1}{5}\Rightarrow\left(a+b\right)\approx101^o\Rightarrow C=79^o\\ c^2=a^2+b^2-2abcosC\Rightarrow c\approx7\)