Question

DAU COROANA!!!!!!!!!!!!!!!!!!! Urgent pls

Answer 1

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]