Prove the Laws of Sines and Cosines and use them to solve problems.
Classify and interpret a solved triangle result
Problem
A solved survey triangle gives a landmark separation of \(12.4~\text{km}\). Classify the result as valid, ambiguous, or impossible and interpret it in context.
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What this problem is really about
Interpret a solved value by naming the physical quantity and carrying its units into the conclusion. Then test the restrictions relevant to that quantity and triangle: lengths must be positive, angle data must be consistent, and any claimed ambiguity needs distinct valid configurations. A decimal measurement alone is not evidence of ambiguity.
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