\(\dfrac{a}{\sin \text{A}} = \dfrac{b}{\sin \text{B}}\)

\(\dfrac{a}{\sin 60^{\circ}} = \dfrac{4\sqrt{2}}{\sin 45^{\circ}}\)

\(\dfrac{a}{\frac{1}{2}\sqrt{3}} = \dfrac{4\sqrt{2}}{\frac{1}{2}\sqrt{2}}\)

\(\dfrac{a}{\cancel{\frac{1}{2}}\sqrt{3}} = \dfrac{4\cancel{\sqrt{2}}}{\cancel{\frac{1}{2}}\cancel{\sqrt{2}}}\)

\(\dfrac{a}{\sqrt{3}} = \dfrac{4}{1}\)

\(a = 4\sqrt{3}\)

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°