Aturan Sinus

\(\dfrac{a}{\sin \text{A}} = \dfrac{b}{\sin \text{B}}\) \(\dfrac{a}{\sin 60^{\circ}} = \dfrac{4\sqrt{2}}{\sin 45^{\circ}}\) \(\dfrac{a}{\frac{1}{2}\sqrt{3}} = \dfrac{4\sqrt{2}}{\frac{1}{2}\sqrt{2}}\) \(\dfrac{a}{\cancel{\frac{1}{2}}\sqrt{3}} = \dfrac{4\cancel{\sqrt{2}}}{\cancel{\frac{1}{2}}\cancel{\sqrt{2}}}\) \(\dfrac{a}{\sqrt{3}} = \dfrac{4}{1}\) \(a = 4\sqrt{3}\) Jadi, panjang sisi BC = \(a = 4\sqrt{3}\)

Jumlah sudut dalam segitiga ABC = 180° A + B + C = 180° 30° + B + 120° = 180° B + 150° = 180° B = 180° − 150° B = 30° Karena besar sudut B adalah 30°, maka jenis segitiga ABC adalah sama kaki dengan AC = BC. Oleh karena itu, panjang sisi BC = \(a = 12\)   \(\dfrac{b}{\sin \text{B}} = \dfrac{c}{\sin \text{C}}\) \(\dfrac{12}{\sin 30^{\circ}} = \dfrac{c}{\sin 120^{\circ}}\) \(\dfrac{12}{\frac{1}{2}} = \dfrac{c}{\sin (180^{\circ}\:-\: 60^{\circ})}\) \(\dfrac{12}{\frac{1}{2}} = \dfrac{c}{\sin 60^{\circ}}\) \(\dfrac{12}{\cancel{\frac{1}{2}}} = \dfrac{c}{\cancel{\frac{1}{2}}\sqrt{3}}\) \(c = 12\sqrt{3}\) Jadi, panjang sisi AB = \(c = 12\sqrt{3}\)

\(\dfrac{a}{\sin \text{A}} = \dfrac{c}{\sin \text{C}}\) \(\dfrac{5\sqrt{2}}{\sin 135^{\circ}} = \dfrac{5}{\sin \text{C}}\) \(\dfrac{5\sqrt{2}}{\sin (180^{\circ}\:-\:45^{\circ})} = \dfrac{5}{\sin \text{C}}\) \(\dfrac{5\sqrt{2}}{\sin 45^{\circ}} = \dfrac{5}{\sin \text{C}}\) \(\dfrac{5\sqrt{2}}{\frac{1}{2}\sqrt{2}} = \dfrac{5}{\sin \text{C}}\) \(\dfrac{5\cancel{\sqrt{2}}}{\frac{1}{2}\cancel{\sqrt{2}}} = \dfrac{5}{\sin \text{C}}\) \(\dfrac{\cancel{5}}{\frac{1}{2}} = \dfrac{\cancel{5}}{\sin \text{C}}\) \(\sin \text{C} = \dfrac{1}{2}\) \(\text{C} = 30^{\circ}\) Jadi, besar sudut C adalah 30°