Measurement applications: sine rule

Task goals

• Apply the sine rule (a/sinA = b/sinB = c/sinC) to find a missing side of a non-right-angled triangle in a real-world measurement scenario, given two angles and one side.
• Find a triangle's third angle using the 180-degree angle sum when two angles are already known, and use that third angle within the sine rule.
• Apply the sine rule directly to find a missing angle from two given sides and a non-included angle, ONLY when the specific numbers are confirmed to be an unambiguous (non-SSA-ambiguous) case, and explain why that case is safe.
• Correctly match each side to the angle it is opposite, recognising that this changes which sine-rule fraction pair is used.
• Decide, from a real-world description or an unlabelled diagram, whether two angles and a side, or two sides and an angle, have been given, and choose the correct sine-rule approach.
• Use a length or angle found with the sine rule as an input to a further measurement, cost, time, or compliance calculation, never leaving a bare "find x" answer unused.
• Convert between units of length before or after applying the sine rule, and round an irrational answer to a stated number of decimal places or degrees without losing precision partway through a multi-step calculation.
• Check a calculated angle or side against a legal minimum/maximum, a stability limit, or a required frontage, and state whether a real-world structure or subdivision complies.
• Combine a sine-rule step with SOHCAHTOA (from the previous LO) within the same problem when genuinely useful, such as decomposing an oblique triangle's side into a vertical height, and cross-checking that height using the triangle's other known side and angle.
• Compare two real material, supplier, or method options using sine-rule-derived numbers, check a stated budget, and write a short, numbers-based justification for a real-world measurement decision.