a) [tex]AC ^{2}=BC ^{2} -AB ^{2} \\
AC ^{2}=100-36=64 \\
AC=8 \\
sinC= \frac{AB}{BC}= \frac{6}{10}= \frac{3}{5} \\
cosC= \frac{AC}{BC}= \frac{8}{10} = \frac{4}{5} \\
tgB= \frac{AC}{AB} = \frac{8}{6}= \frac{4}{3} \\
ctgB= \frac{1}{tgB} = \frac{3}{4} [/tex]
b)[tex] BC^{2}= AB^{2} + AC^{2} =25+75=100 \\
BC=10 \\
sinB= \frac{5 \sqrt{3} }{10} = \frac{ \sqrt{3} }{2} \\
cosB= \frac{5}{10}= \frac{1}{2} \\
tgC= \frac{5}{5 \sqrt{3} }= \frac{1}{ \sqrt{3} } = \frac{ \sqrt{3} }{3} \\
ctgC= \frac{5 \sqrt{3} }{5}= \sqrt{3} [/tex]
c)[tex]sinC= \frac{AB}{BC} \\
\frac{3}{5} = \frac{AB}{25} \\
AB= \frac{25*3}{5}=15 \\ \\
AC^{2}= BC^{2}- AB^{2} \\ \\
AC^{2} =625-225=400 \\
AC=20 \\
cosB= \frac{AC}{BC} = \frac{4}{5} \\
ctgC= \frac{AC}{AB}= \frac{4}{3} [/tex]
