$AC^2=BC^2+AB^2-2BC.AB\cos B$
$\to 4^2=5^2+AB^2-2.5.AB\cos 30^o$
$\to AB^2-5\sqrt3.AB+9=0$
$\to AB\approx 7,45$
$\dfrac{BC}{\sin A}=\dfrac{AC}{\sin B}$
$\to \sin A=\dfrac{5}{8}$
$\to A\approx 38^o40'$
$S_{ABC}=\dfrac{1}{2}BC.AB\sin B=9,3125$
$p=\dfrac{AB+AC+BC}{2}=8,225$
$\to r=\dfrac{S}{P}\approx 1,132$
$S=\dfrac{AB.AC.BC}{4R}$
$\to R=\dfrac{AB.AC.BC}{4S}=4$
$S_{ABC}=\dfrac{1}{2}.AB.h_c$
$\to h_c=2,5$
$m_b=\sqrt{ \dfrac{BC^2+BA^2}{2}-\dfrac{AC^2}{4}}\approx 6$
