Bearer100
A. AB/Sin C = BC/Sin A 30/Sin 120° = BC/Sin 30° 30/(½√3) = BC/(½) 15 = ½√3 BC 30/√3 = BC 10√3 = BC
∠B = 180° − ∠A − ∠B ∠B = 180° − 120° − 30° = 30°
Luas = ½ × AB × BC × Sin B Luas = ½ × 30 × 10√3 × Sin 30° Luas = 75√3
b. AC/Sin B = BC/Sin A 18/Sin 60° = 10/Sin A 18/(½√3) = 10/Sin A 18 Sin A = 5√3 Sin A = 5√3/18
Sin C = Sin (180 − A −B) Sin C = Sin (180 − (A +B)) Sin C = Sin (A + B) Sin C = Sin A Cos B + Sin B Cos A Sin C = 5√3/18 ∙ 1/2 + ½√3 ∙ √249/18 Sin C = (5√3 + 3√83)/18
Luas = ½ AC BC Sin C Luas = ½∙18∙10∙(5√3 + 3√83)/18 Luas = 25√3 + 15√83
AB/Sin C = BC/Sin A
30/Sin 120° = BC/Sin 30°
30/(½√3) = BC/(½)
15 = ½√3 BC
30/√3 = BC
10√3 = BC
∠B = 180° − ∠A − ∠B
∠B = 180° − 120° − 30° = 30°
Luas = ½ × AB × BC × Sin B
Luas = ½ × 30 × 10√3 × Sin 30°
Luas = 75√3
b.
AC/Sin B = BC/Sin A
18/Sin 60° = 10/Sin A
18/(½√3) = 10/Sin A
18 Sin A = 5√3
Sin A = 5√3/18
Sin C = Sin (180 − A −B)
Sin C = Sin (180 − (A +B))
Sin C = Sin (A + B)
Sin C = Sin A Cos B + Sin B Cos A
Sin C = 5√3/18 ∙ 1/2 + ½√3 ∙ √249/18
Sin C = (5√3 + 3√83)/18
Luas = ½ AC BC Sin C
Luas = ½∙18∙10∙(5√3 + 3√83)/18
Luas = 25√3 + 15√83