Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
B{C^2} = A{B^2} + A{C^2} + 2.AB.AC.\cos A\\
= 25 + 36 + 2.5.6.\cos \left( {90 + \frac{{\angle B}}{2}} \right)\\
\cos B = \frac{{A{B^2} + B{C^2} - A{C^2}}}{{2.AB.BC}} = \frac{{25 + 25 + 36 + 2.5.6.\cos \left( {90 + \frac{{\angle B}}{2}} \right) - 36}}{{2.5.\sqrt {25 + 36 + 2.5.6.\cos \left( {90 + \frac{{\angle B}}{2}} \right)} }}\\
= \frac{{50 + 60.\sin \frac{B}{2}}}{{10\sqrt {61 + 60.\sin \frac{B}{2}} }}\\
\to \angle B = 38.94244127^\circ \\
\to B{C^2} = 41 \to BC = \sqrt {41}
\end{array}\)
