Jika 3 sin a + 4 cos a = 5 , maka nilai sin a adalah ... A. 0,50 B. 0,60 C. 0,75 D. 0,8 E. 1,2

[tex]3 \sin(a) + 4 \cos(a) = 5 \\ 4( \sqrt{1 - {sin}^{2}a} ) = 5 - 3 \sin(a) \\ \sqrt{1 - {sin}^{2}a} = \frac{5 - 3 \sin(a) }{4} \\ 1 - {sin}^{2} a = \frac{9 {sin}^{2}a - 30 \sin(a) + 25}{16} \\ 16 - 16 {sin}^{2} a = 9 {sin}^{2} a - 30 \sin(a) + 25 \\ 25 {sin}^{2} a - 30 \sin(a) + 9 = 0 \\ {(5 \sin(a) - 3)}^{2} = 0 \\ \sin(a) = \frac{3}{5} = 0.60[/tex]