Pada segitiga ABC dengan sinA = 3:5 dan sinB = 1:2 maka cosC =

Perhatikan bahwa
A + B + C = 180°
C = 180° - (A + B)
sin C = sin (180° - (A + B))
sin C = sin (A + B)

[tex] sin A = \frac{3}{5} \\ cos A = \frac{\sqrt{5^2-3^2}}{5} \\ cos A = \frac{4}{5} \\ sin B = \frac{1}{2} \\ cos B = \frac{\sqrt{2^2-1^2}}{2} \\ cos B = \frac{\sqrt{3}}{2} \\ sin (A+B) = sin C \\ sin A.cos B + sin B.cos A = sin C \\ sin C = \frac{3}{5}.\frac{\sqrt{3}}{2} + \frac{1}{2}.\frac{4}{5} \\ sin C = \frac{3\sqrt{3}}{10} + \frac{4}{10} \\ sin C = \frac{3\sqrt{3} + 4}{10} \\ {} \\ cos C = \frac{\sqrt{10^2-(3\sqrt{3}+4)^2}{10} \\ cos C = \frac{\sqrt{100-(27+16+24\sqrt{3})}}{10} \\ cos C = \frac{\sqrt{57+2\sqrt{432}}{10} \\ cos C = \frac{\sqrt{9}+\sqrt{48}}{10} \\ cos C = \frac{3+4\frac{3}}{10} [/tex]