(Trigonometri) Luas segitiga ABC pada gambar berikut adalah=… cm^2
Jawaban Terkonfirmasi
Materi Trigonometri
Kelas X
sin 105° = sin(45° + 60°)
= sin 45° cos 60° + sin 60° cos 45°
= ½√2 × ½ + ½√3 × ½√2
= ¼√2 + ¼√6
∠ C = 180° – (105° + 30°)
∠ C = 180° – 135°
∠ C = 45°
BC / sin 105° = AC / sin 30°
4 / (¼√2 + ¼√6) = AC / ½
AC = (2√6 – 2√2) cm
L = ½ × AC × BC × sin C
L = ½ × (2√6 – 2√2) × 4 × sin 45°
L = 2(2√6 – 2√2) × ½√2
L = √2 × (2√6 – 2√2)
L = 2√12 – (2 × 2)
L = 2 × 2√3 – 4
L = 4√3 – 4
L = 4(√3 – 1) cm²