\(\begin{array}{l} a)\,\,\,Ta\,\,có:\,\,\,A{B^2} = {6^2} = 36;\,\,A{C^2} = {8^2} = 64;\,\,B{C^2} = {10^2} = 100\\ \Rightarrow A{B^2} + A{C^2} = 36 + 64 = 100 = B{C^2}\\ \Rightarrow \Delta ABC\,\,vuông\,\,tại\,\,A\,\,\,\left( {Định\,\, lý\,\,Pitago\,\,đảo} \right).\\ b)\,\,\sin \widehat B = \dfrac{{AC}}{{BC}} = \frac{8}{{10}} = \dfrac{4}{5}\\ \cos \widehat B = \dfrac{{AB}}{{BC}} = \dfrac{6}{{10}} = \dfrac{3}{5}\\ \tan \widehat B = \dfrac{{AC}}{{AB}} = \dfrac{8}{6} = \dfrac{4}{3}\\ \cot \widehat B = \dfrac{{AB}}{{AC}} = \dfrac{6}{8} = \dfrac{3}{4}. \end{array}\)
