Răspuns:
5. sin B= AC/BC => BC= AC/sin 60= 8* [tex]\frac{2}{\sqrt{3} }[/tex]= [tex]\frac{16 \sqrt{3} }{3}[/tex]cm
cos B= AB/BC=> AB= BC* cos 60 = [tex]\frac{16 \sqrt{3} }{3}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{8 \sqrt{3} }{3}[/tex] cm
[tex]AC^{2}[/tex]= CD*BC => CD= 64* [tex]\frac{ 3}{16 \sqrt{3}}[/tex] = 4*3 / [tex]\sqrt{3}[/tex]= 12
[tex]AB^{2}[/tex]= BD*BC => BD= [tex]\frac{64*3}{9}[/tex] * [tex]\frac{ 3}{16 \sqrt{3}}[/tex] = [tex]\frac{4}{\sqrt{3} }[/tex]= [tex]\frac{4\sqrt{3} }{3}[/tex] cm
[tex]AD^{2}[/tex]= CD* BD= [tex]\frac{4\sqrt{3} }{3}[/tex] * [tex]4\sqrt{3}[/tex] = 16* 3/3 = 16 cm
AD= [tex]\sqrt{16}[/tex]= 4 cm
