diketahui segitiga ABC sama kaki, AB=AC dan sudut BAC = 30 drajat. jika panjang BC = 4 cm, maka luas segitiga ABC

Matematika X SMA
→→ Luas Segitiga ←←

Pembahasan :
Sudut sama kaki nya = (180° - 30)/2 = 75°

Sin 75°
= Sin (90 - 15)°
= Cos 15°
= Cos (45 - 30)°
= Cos 45° Cos 30° + Sin 45° Sin 30°
= (1/2 √2)(1/2 √3) + (1/2 √2)(1/2)
= (1/4 √6) + (1/4 √2)
= 1/4(√6 + √2)

Aturan Sinus
BC/Sin A = AB/Sin C
4/Sin 30° = AB/Sin 75°
8Sin 75° = AB
AB = 8[1/4(√6 + √2)]
AB = 2(√6 + √2) cm

Luas Segitiga = 1/2 . AB . AC Sin A
Luas Segitiga = 1/2 (2√6 + 2√2)² (1/2)
Luas Segitiga = 1/4(32 + 16√3)
Luas Segitiga = (8 + 4√3) cm²

<ABC = <ACB = (180 - 30)/2 = 75°

AB/sin C = BC/sin 75
AB/sin 75 = 4/sin 30
AB = 8 sin 75
AB = 8 × (√6 + √2)/4
AB = 2√6 + 2√2 cm = AC

↓
Luas = 1/2 AB BC sin B
Luas = 1/2  (2√6 + 2√2) . 4 sin 75
Luas = 1/2 (8√6 + 8√2) × (√6 + √2)/4
Luas = (4√6 + 4√2) (√6 + √2)/4
Luas = (24 + 16√3+ 8)4
Luas = (32 + 16√3)/4
Luas = 8 + 4√3 cm²