Răspuns:
[tex]\cos C = -\frac{3}{5}[/tex]
Explicație pas cu pas:
[tex] A = 16 = \frac{AC \cdot BC \cdot \sin{ACB}}{2} \iff \sin{ACB} = \frac{32}{AC\cdot BC} = \frac{32}{5\cdot 8} = \frac{4}{5}\\ \\ sin^2 ACB + cos^2 ACB = 1\\ \\ cos^2 ACB = 1 - sin^2 ACB \\ \\ \cos {ACB} = \pm \sqrt{1-sin^2 ACB} = \pm \sqrt{1 - \frac{16}{25}}\\ \\ \cos{ACB} = \pm \sqrt{\frac{9}{25}} \\ \\ \cos{ACB} = \pm \frac{3}{5}\\ \\ \textrm{C este obtuz} \iff C \in \textrm{Cadranul 2} \implies \cos C < 0\implies \cos C = -\frac{3}{5}[/tex]