1. 5.7 The Ambiguous Case for the Law of Sines
Objective:
Determine whether a triangle has zero, one, or two possible configurations.
Solve triangles using the Law of Sines.

2. Law of Sines
Let ∆ABC be any triangle with a, b, and c representing the measures of sides opposite angles with measurements A, B, and C, respectively. Then

3. Case A ≥ 90°
A = 110°, a = 10, b = 20
No solution!

4. Case A ≥ 90°
A = 110°, a = 20, b = 10
One solution!

5. Case A < 90°
A = 85°, a = 15, b = 25
No solution!

6. Case A < 90°
A = 30°, a = 5, b = 10
One solution!

7. Case A < 90°
A = 30°, a = 7, b = 10
Two solutions!

8. Case A < 90°
A = 30°, a = 12, b = 10
One solution!

9. Assignment
5.7 Practice Worksheet #5-11
5.7 pg 324 #18, 20, 24, 35