1. Quiz 1) Find side a and Angle C C A=45º c b=12 a B=72º 2) Find the Area A c b=14 a=18 B C=57º

2. Quiz 1) Find side a and Angle C C A=45º c b=12 a B=72º

3. Quiz 2) Find the Area A c b=14 a=18 B C=57º

4. Law of Sines There are special cases where we use the law of sines and we could possibly get two answers It is also possible to get zero answers We use the same proportion for the law of sines – we just have to check one thing at the end to determine if there are multiple answers

5. Law of Sines – no answers Use the law of sines to solve the following triangle for angle B C A=35º B c b=10 a=5

6. Law of Sines – no answers Use the law of sines to solve the following triangle for angle B C A=35º B c b=10 a=5 We solved this by hitting 2 nd sin in our calculator and getting:

7. Law of Sines – no answers Use the law of sines to solve the following triangle for angle B C A=35º B c b=10 a=5 But when we enter this into the calculator we get an error That is because sin can never be larger than one – which means there is no answer to this problem

8. Law of Sines – multiple answers Use the law of sines to solve the following triangle for angle B C A=25º B c b=21 a=10

9. Law of Sines – multiple answers C A=25º B c b=21 a=10 We need to check the possibility that there are two answers – to do this we do the following:

10. Law of Sines – multiple answers C A=25º B c b=21 a=10 Take the angle that we found and subtract from 180º This is our potential 2 nd answer To check to see if it is a potential answer check to see what this angle and the angle we started with (Angle A) add up to

11. Law of Sines – multiple answers C A=25º B c b=21 a=10 Since this is less than 180º - 117.4 is also a possible answer to Angle B. So this problem has 2 answers – 62.6 or 117.4. You should check all law of sine problems to see if this is the case.

12. Law of Sines – multiple answers Find Angle A C A c b=11 a=5 B=105º

13. Law of Sines – multiple answers Find Angle A C A c b=11 a=5 B=105º This is larger than 180 so 154 is not a possible answer There is only one answer to this problem  26º