Matematika

Pertanyaan

diketahui ∆abc . panjang bc = 3 dan ac =5 cm jika sudut ABC =90° . maka nilai cosinus sudut BAC adalah..

2 Jawaban

  • → Cosinus = Sisi samping sudut / sisi miring sudut
    → BC = 3 Cm
    → AC = 5 Cm
    → AB = ...Cm
    → ∠ABC = 90° (Siku - siku)
     
    Cos ∠BAC = Cos ∠A
    ⇒ Cos ∠A = AB / AC
    → AB² = 5² - 3²
    → AB² = 16
    → AB = 4
    ⇒ Cos ∠A = 4/5 
  • Sin = depan / miring = y/r
    Cos = samping / miring = x/r

    Diketahui:
    bc (a) = 3
    ac (b) = 5
    ∠ABC (sinb) = 90° = 1

    Ditanya:
    Cos ∠ BAC = ??

    Pembahasan:
    a/sina = b/sinb
    3/sina = 5/1
    sina = (3 x 1)/5
    sina = 3/5

    x² = r² - y²
    x² = 5² - 3²
    x² = 25 - 9
    x² = 16
    x = √16
    x = 4

    Maka:
    cosinus ∠ BAC:
    = samping/miring
    = x/r
    = 4/5

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