Giải thích các bước giải:
\(\begin{array}{l}
{a^2} = {b^2} + {c^2} - 2.b.c.\cos A = {35^2} + {20^2} - 2.20.35.\cos 60^\circ = 925\\
\Rightarrow a = 5\sqrt {37} \\
{S_{ABC}} = \frac{1}{2}.b.c.\sin A = \frac{1}{2}.35.20.\sin 60^\circ = 175\sqrt 3 \\
{h_a} = \frac{{2{S_{ABC}}}}{a} = \frac{{70\sqrt 3 }}{{\sqrt {37} }} = \frac{{70\sqrt {111} }}{{37}}\\
{S_{ABC}} = \frac{{abc}}{{4R}} \Rightarrow R = \frac{{5\sqrt {111} }}{3}\\
{S_{ABC}} = \frac{{a + b + c}}{2}.r \Rightarrow r = \frac{{350\sqrt 3 }}{{55 + 5\sqrt {37} }}
\end{array}\)
