a.
\(cosA=\dfrac{b^2+c^2-a^2}{2bc}=\dfrac{\sqrt{3}}{12}\)
\(\Rightarrow A\simeq81^042'\)
\(cosB=\dfrac{a^2+c^2-b^2}{2ac}=\dfrac{5\sqrt{2}}{12}\)
\(\Rightarrow B\simeq53^053'\)
\(S=\dfrac{1}{2}bc.sinA=\dfrac{1}{2}.2\sqrt{3}.sin81^042'\simeq1,71\)
\(\Rightarrow h_a=\dfrac{2S}{a}\simeq1,4\)
\(R=\dfrac{a}{2sinA}=\dfrac{\sqrt{6}}{2sinA}=1,24\)
b.
\(cosA=\dfrac{b^2+c^2-a^2}{2bc}=\dfrac{1}{2}\Rightarrow A=60^0\)
\(cosB=\dfrac{a^2+c^2-b^2}{2ac}=\dfrac{11}{14}\)
\(\Rightarrow B\simeq38^012'\)
\(S=\dfrac{1}{2}bc.sinA=\dfrac{1}{2}.5.8.sin60^0=10\sqrt{3}\)
\(\Rightarrow h_a=\dfrac{2S}{a}=\dfrac{20\sqrt{3}}{7}\)
\(R=\dfrac{a}{2sinA}=\dfrac{7\sqrt{3}}{3}\)
