Matematika

Pertanyaan

1. Tentukan aturan sinus:
a) b)
2. Tentukan aturan consinus:
a) a=6 b=5 b) b=7 c=6

Tolong bantu kerjain ya. Terimakasih

1 Jawaban

  • 1. a) a/sin A = b/sin B
            5 cm/sin 30° = b/sin 60°
            5/¹/₂ = b/¹/₂√3
            10 = b/¹/₂√3
            b = 10 . ¹/₂√3
               = 5√3 cm

            C = 180° - (30° + 60°)
                = 180° - 90°
                = 90°

            c/sin C = a/sin A
            c/sin 90° = 5 cm/sin 30°
            c/1 = 5/¹/₂
            c = 10 cm

        b) a/sin A = b/sin B
            a/sin 90° = 6 cm/sin 30°
            a/1 = 6/¹/₂ 
            a = 12 cm

            C = 180° - (30° + 90°)
                = 180° - 120°
                = 60°        
     
            c/sin C = a/sin A
            c/sin 60° = 12 cm/sin 90°
            c/¹/₂ = 12
            c = 6 cm

    2. a) a/sin A = b/sin B
            6/sin 30° = 5/sin B
            6/¹/₂ = 5/sin B
            sin B = 5/12
            B = 25°
              
            C = 180° - (30° + 25°)
               = 180° - 55°
               = 125°

            c/sin C = a/sin A
            c/sin 125° = 6/sin 30°
            c/0,85 = 5/¹/₂
            c = 8,5

            b/sin B = c/sin C
            7/sin B = 6/sin 45°
                        = 6/¹/₂√2
                        = 6√2
            sin B = 7/6√2
                     = 0,824
            B = 55°

            A = 180° - (55° + 45°)
               = 180° - 90°
               = 90°

            a/sin A = c/sin C
            a/sin 90° = 6 cm/sin 45°
            a/1 = 6/¹/₂√3 
            a = 4√3

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