Question 1081192: What do they mean by which of the following settings does a uniquely determined triangle ABC exist?
The options were,
A) AB = 11, BC = 19, CA = 7
B) AB = 11, BC = 6, Angle BAC = 63°
C) AB = 11, CA = 7, Angle CBA = 128°
D) AB = 11, Angle BAC = 63°, Angle CBA = 128°
E) None of these
According the SSS, AAS, SAS, ASA, rules, (I'm not sure what they're called).
Only A and C work? But there is only one answer?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A) describes an impossible triangle because AB+AC
D) is also impossible, because it has 2 angles whose measures add up to more than 180 degrees. not so
C) also describes an impossible triangle. It has an obtuse angle at B, so that is the largest angle, meaning that opposite side AC should be the longest side, but it is shorter than AB.
B) is also impossible. If you try to construct it, you realize that a line passing through A, at a 63 degree angle with AB,will never intersect short side CA.
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