Pada segitiga ABC , sisi a = 7 cm , b = 3 cm dan c = 5 cm . Nilai sin a adalah....... A. -1/2 √3 B. - 1/2√2 C. 1/2 D. 1/2√2 E. 1/2√3

a^2 = b^2 + c^2 - 2bc cos A
7^2 = 3^2 + 5^2 - 2.3.5 cos A
49 = 9 + 25 - 30 cos A
30 cos A = 9 + 25 - 49
Cos A = -15/30 = -1/2 => cos 120°

Sin A = sin 120° = sin 60° = 1/2 √3

Matematika X SMA
Trigonometri

Pembahasan :
Aturan Cosinus

a² = b² + c² - 2bc Cos A
7² = 3² + 5² - 2(3)(5) Cos A
49 = 9 + 25 - 30 Cos A
49 = 34 - 30Cos A
30Cos A = 34 - 49
30Cos A = -15
Cos A = -15/30
Cos A = -1/2

Berdasarkan Identitas Trigonometri
Sin²A + Cos²A = 1
Sin²A = 1 - Cos²A
Sin A = √[1 - Cos²A]
Sin A = √[1 - (-1/2)²]
Sin A = √[1 - 1/4]
Sin A = √[3/4]
Sin A = 1/2 √3