a: \(AC=\sqrt{5^2-3^2}=4\left(cm\right)\)
\(\sin B=\cos C=\dfrac{AC}{BC}=\dfrac{4}{5}\)
\(\sin C=\cos B=\dfrac{AB}{BC}=\dfrac{3}{5}\)
\(\tan B=\cot C=\dfrac{AC}{AB}=\dfrac{4}{3}\)
\(\cot B=\tan C=\dfrac{3}{4}\)
b: \(AB=\sqrt{13^2-12^2}=5\left(cm\right)\)
\(\sin B=\cos C=\dfrac{AC}{BC}=\dfrac{12}{13}\)
\(\sin C=\cos B=\dfrac{AB}{BC}=\dfrac{5}{13}\)
\(\tan B=\cot C=\dfrac{AC}{AB}=\dfrac{12}{5}\)
\(\cot B=\tan C=\dfrac{5}{12}\)
c: \(BC=\sqrt{4^2+3^2}=5\left(cm\right)\)
\(\sin B=\cos C=\dfrac{AC}{BC}=\dfrac{4}{5}\)
\(\sin C=\cos B=\dfrac{3}{5}\)
\(\tan B=\cot C=\dfrac{4}{3}\)
\(\tan C=\cot B=\dfrac{3}{4}\)