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Aturan sinus dan cosinus

1.
sin B /b = sin A/ a
sin B = (b/a) . sin A
sin B = 5/8. sin 37 = 0,376
<B = sin⁻¹ (0,376) = 22

<C = 180 - <A - <B = 121

c² = a²+b² - 2ab cos C
c² = 64 + 25 - 2(8)(5) cos 121
c² = 89 - 80 (-0,51) = 129,8
c = 11,39

2.
<B = 180 - <A - <C
<B = 10
,
a/sin A = c/sin C
c=  a. sin C/ sin A = (200)(sin 20)/(sin 150)
c = (200x0,34)/ (1/2) = 400x 0,34
c = 136
.
b/sin B = a/sin A --> b =  (a . sin B)/(sin A)
b = (200 x sin 10)/sin 150 = (200 x 0,17)/(0,5)
b = 400x 0,17
b = 68


2) cos A = (AB²+AC² - BC²) / (2 (AB)(AC)
cos A = (81+64 - 49)/ (2)(9)(8) = 96/(2)(9)(8)= 96/144
cos A = 2/3

sin A = √(1 - cos² A) = √(1-4/9) = √(5/9) = 1/3 √5
tan A = sin A/ cos A = 1/3 √5  : (2/3)  = 1/2 √5