\(\sin\widehat{B}=\cos\widehat{C}=\dfrac{AH}{AB}=\dfrac{6}{2\sqrt{13}}=\dfrac{3\sqrt{13}}{13}\)
\(\cos\widehat{B}=\sin\widehat{C}=\dfrac{2\sqrt{13}}{13}\)
\(\tan\widehat{B}=\cot\widehat{C}=\dfrac{3}{2}\)
\(\tan\widehat{C}=\cot\widehat{B}=\dfrac{2}{3}\)