a) p=[tex] \frac{AB+BC+AC}{2}= \frac{24 \sqrt{2} }{2}=12 \sqrt{2} [/tex]
A=[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]=[tex] \sqrt{12 \sqrt{2}*8 \sqrt{2}*3 \sqrt{2}* \sqrt{2} } [/tex]=[tex] \sqrt{12*8*3*2*2}=\sqrt{36*4*8}= 6*2*2\sqrt{2}=24 \sqrt{2} [/tex]
b)A=[tex] \frac{AB*AC*sin(A) } {2} [/tex]=36*sin(A)=>sin(A)=[tex] \frac{24 \sqrt{2} }{36}= \frac{2 \sqrt{2} }{3} [/tex]
cos(A)=[tex] \sqrt{1- (sin(A))^{2} }= \sqrt{1- \frac{8}{9} }= \sqrt{ \frac{1}{9} }= \frac{1}{3} [/tex]
tg(A)=[tex] \frac{sin(A}{cos(A)}= \frac{ \frac{2 \sqrt{2} }{3} }{ \frac{1}{3} } =2 \sqrt{2} [/tex]
ctg(A)=[tex] \frac{cos(A)}{sin(A)}= \frac{ \frac{1}{3} }{ \frac{2 \sqrt{2} }{3} }= \frac{ \sqrt{2} }{4} [/tex]
