jika segitiga ABC diketahui AC =10/3√6 cm,BC=10cm,dan sudut A =60°,maka panjang BC adalah.

Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri

Pembahasan :
Aturan Sinus

AC/Sin B = BC/Sin A
(10/3 √6)/Sin B = 10/Sin 60°
(10/3 √6)(1/2 √3) = 10Sin B
10/6 √9.2 = 10Sin B
5/3 . 3 √2 = 10Sin B
5√2 = 10Sin B
Sin B = 1/2 √2
B = 45°

AB/Sin C = BC/Sin A
AB/Sin 75° = 10/Sin 60°
AB = 10/(1/2 √3) . Sin 15°
AB = 20/3 √3 [1/4(√6 - √2)]
AB = (15√2 - 5√6)/3 cm