Question

City A is 300km due east of City B. City C is 200km on a bearing of 123° from City B. How far is it from City C to City A?

Answer 1

The cosine rule gives

$$AC=\sqrt{AB^2+BC^2-2AB*BC*\cos (33^\circ)}$$

$$AC=\sqrt{300^2+200^2-2*300*200*\cos (33^\circ)}$$

$$AC=171.3\:\rm km$$