Answer:
D) Two triangles can be formed where angle B is 40° or 140°.
Step-by-step explanation:
The Ambiguous Case for the Law of Sines occurs when one uses it to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). There are 6 cases:
Case 1: If ∠A is acute, and a < h, no such triangle exists
Case 2: If ∠A is acute, and a = h, one possible triangle exists
Case 3: If ∠A is acute, and a > b, one possible triangle exists.
Case 4: If ∠A is acute, and h < a < b, two possible triangles exist.
Case 5: If ∠A is obtuse, and a < b or a = b, no such triangle exists.
Case 6: If ∠A is obtuse, and a > b, one such triangle exists.
Here, we can see that ∠A is acute since 75°<90°
Also, we know that a < b since 2 < 3.
Thus, Case 4 applies here, which states "If ∠A is acute, and h < a < b, two possible triangles exist."
Thus, the last option is correct.
Read more:
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/EMAT%206700/law%20of%20sines/Law%20of%20Sines%20ambiguous%20case/lawofsinesambiguouscase.html
Answer:
It's D
Two triangles can be formed where angle B is 40° or 140°
Step-by-step explanation:
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