Matematika

Pertanyaan

1. jika A + B=phi/6 dan cos A . cos B =3/4 , cos (A-B)=......
2. segitiga ABC dg sudu ACB=105derajat, sudut ABC=45derajat, dan AB =(akar 2 + akar6 )cm. panjang sisi BC=....?
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1 Jawaban

  • Trigonometri
    Gunkana rumus 
    2 cos A cos B = cos (A+B) + cos (A - B)
    2 (3/4) = cos π/6 + cos (A - B)
    3/2 = 1/2 √3 + cos (A - B)
    cos (A - B) = 3/2  - 1/2 √3
    cos (A - B ) = 1/2 ( 3 - √3)

    2. <A + <B + <C = 180
    <A = 180 - <B - <C
    <A = 180 - 45 -105
    <A = 30
    aturan sinus   BC/ sin A =  AB/ sin C
    BC  = (AB)(sin A)/ sin C
    BC = (√2 + √6)(sin 30) / sin 105
    BC  = (√2 + √6)(1/2)/ sin (60+45)
    BC = 1/2 (√2 +√6) / (1/4 (√2 + √6))
    BC =(1/2) /(1/4)
    BC = 1/2 x 4/1 = 4/2
    BC  = 2 cm

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