Exploration 1. Case #1

Exploration 1. Case #2, 3

Exploration 2. Case #1, 2

Exploration 2. Case #3

Exploration 3.

Question 1: Explain why sin C is the same in both triangles in the ambiguous case (exploration 3). This is why the Law of Sines is also ambiguous in this case.

SinC is the same in both triangle because SinA remains the same since according to the law of sin, sinA= sinC.

Question 2: What did you discover about the number of triangles you can make given SSA (two sides and an angle)? Summarize the "rules" for all cases.

Exploration 1. Case #2, 3

Exploration 2. Case #1, 2

Exploration 2. Case #3

Exploration 3.

Question 1: Explain why sin C is the same in both triangles in the ambiguous case (exploration 3). This is why the Law of Sines is also ambiguous in this case.

SinC is the same in both triangle because SinA remains the same since according to the law of sin, sinA= sinC.

Question 2: What did you discover about the number of triangles you can make given SSA (two sides and an angle)? Summarize the "rules" for all cases.

**If angel A is obtuse and...**

- BC > AB....1 triangle

- BC = AB....0 triangle
- BC <>

- BC <>
- BC = h....1 triangle
- BC > AB > h....1 triangle
- AB > BC > h....2 triangles

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