*Tính $S:$
$S_{ΔABC}=\frac{1}{2}.b.c.sinA=\frac{1}{2}.8.5.sin60^o=10\sqrt{3}$
*Tính $R:$
$a^2=b^2+c^2-2bc.cosA=8^2+5^2-2.8.5.cos60^o$
$⇔a^2=49$
$⇔a=\sqrt{49}=7$
$S_{ΔABC}=\frac{abc}{4R}⇔10\sqrt{3}=\frac{7.8.5}{4R}$
$⇔R=\frac{7.8.5}{4.10\sqrt{3}}=\frac{7\sqrt{3}}{10}=3$
*Tính $r:$
$S_{ΔABC}=p.r⇔10\sqrt{3}=10.r$
$⇔r=\frac{10\sqrt{3}}{10}=\sqrt{3}$
*Tính $h_a:$
$S_{ΔABC}=\frac{1}{2}a.h_a⇔10\sqrt{3}=\frac{1}{2}.7.h_a⇔10\sqrt{3}.\frac{2}{7}=\frac{20\sqrt{3}}{7}$
*Tính $m_a:$
$(m_a)^2=\frac{b^2+c^2}{2}-\frac{a^2}{4}=\frac{8^2+5^2}{2}-\frac{7^2}{4}=\frac{129}{4}$
$⇔m_a=\sqrt{\frac{129}{4}}=\frac{\sqrt{129}}{2}$
