1) Sin= 8/10 dan sudut A tumpul, nilai 2 sin A.cos A? 2) pjg AB, BC, AC berturut2 adlh 6,5,4 cm. Nilai sin sudut ACB?

Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri

Pembahasan :
1|| Sin A = 4/5

Depan = 4
Miring = 5
Samping = - 3 (Triple Pythagoras)

Maka...
2Sin A Cos A
= 2(4/5)(-3/5)
= -(24/25)

2|| Aturan Cosinus

Cos ACB = (AC² + BC² - AB²)/2.AC.BC
Cos ACB = (4² + 5² - 6²)/2(20)
Cos ACB = (16 + 25 - 36)/40
Cos ACB = 5/40
Cos ACB = 1/8

Identitas Trigonometri
Sin²C + Cos²C = 1
Sin ACB = √[1 - (Cos ACB)²]
Sin ACB = √[1 - (1/8)²]
Sin ACB = √[1 - (1/64)]
Sin ACB = √[63/64]
Sin ACB = 3/8 √7