Applying the Sine and Cosine Rules to Non-Right-Angled Triangles

Task goals

• Foundation: Use the sine rule to find an unknown side or angle in a non-right-angled triangle given two angles and one side, or two sides and a non-included angle.
• Proficient: Apply the cosine rule to find an unknown side or angle when given two sides and the included angle (or three sides), and calculate triangle area using $\tfrac{1}{2}ab\sin C$.
• Excellence: Solve multi-step contextual problems (e.g. navigation, surveying, structural design) that require choosing between the sine rule, cosine rule and area formula, and recognising the ambiguous case.