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Which set of given measurements can produce two different triangles?
ATwo angles and the included side
BTwo angles and any one side
CThree angles with no side
DTwo sides and a non-included angle
Answer & Solution
Correct answer: D. Two sides and a non-included angle
1. Two sides with the angle opposite one of them is the SSA arrangement.
2. The unknown side can swing to two different positions and still fit the data.
3. That is why SSA is called the ambiguous case, with zero, one or two triangles possible.
4. Two angles with any side fixes the third angle and scales the triangle uniquely.
_Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.1 Non-right Triangles: Law of Sines_