1. Math 150 7.1/7.2 – The Law of Sines 1

2. Q: We know how to solve right triangles using trig, but how can we use trig to solve any triangle? A: The Law of Sines (7.1/7.2) and The Law of Cosines (7.3). 2

3. Q: We know how to solve right triangles using trig, but how can we use trig to solve any triangle? A: The Law of Sines (7.1/7.2) and The Law of Cosines (7.3). 3

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7. To solve a triangle, we’ve needed to know some of its sides and angles. We can classify the possibilities like this (A = Angle, S = Side): Case 1: ASA or SAA 7

8. Case 2: SSA 8

9. Case 3: SAS 9

10. Case 4: SSS 10

11. Note: The Law of Sines helps us solve cases 1 and 2. The Law of Cosines helps us solve cases 3 and 4. 11

12. 12 Pain in the SSA

13. 13 Pain in the SSA

14. 14 Pain in the SSA

15. 15 Pain in the SSA

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22. 22 Area of a Triangle (SAS)

23. 23 Area of a Triangle (SAS)

24. 24 Area of a Triangle (SAS)

25. 25 Area of a Triangle (SAS)

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31. Let’s go back and prove the Law of Sines as well… 31

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