1. MM4A6c: Apply the law of sines and the law of cosines.

2. Essential Question:
How do I solve problems using the Law of Cosines?

3. Law of Cosines
To find the length of a missing side of a triangle, add the sum of the squares of the other 2 sides and subtract twice the product of the other 2 sides and the cosine of the included angle.

4. Law of Cosines

5. Rules… Must have SSS or SAS information
The side that begins the formula will be the same as the angle that ends the formula.
Always find the largest angle of the triangle first using the Law of Cosines, then use the Law of Sines to complete the problem if possible.

6. Rules continued…
REMEMBER: when looking for an angle measure, you take the INVERSE of the value.
If you get an error message, and you have rechecked your work, the answer is DNE. The reason for that is sometimes the given information cannot form a real triangle.

7. Example 1
a=123, c=97, B=22°, find b

8. Example 2
a=11.3, b=7.2, c=14.8, find A

9. Example 3
c=5.1, B=81°, a=4.7
Solve the triangle using the Law of Cosines and the Law of Sines

10. Example 4
Using info given from Example 2, solve the triangle: a=11.3, b=7.2, c=14.8, A=48°
HINT: always use the Law of Cosines to find the largest angle first, then use the Law of Sines to solve the triangle.

11. Homework/Class work Page 899 9-24 all
When possible, start with the biggest angle or side length

12. Do Now
Solve the triangle: c=7.1, B=29°, a=10 *Use the Law of Cosines to create a ratio, THEN use the Law of Sines to solve*

14. Do Now #2
Solve the triangle: a=8, b=12.1, c=9.4

16. Pg. 899, 9-23 ODD SAS; A=53° 11. SSS; A=88° 13. SAS; c=7.1
15. SAS; b=34
17. SAS; a=4.1
19. A=44°, B=74°, C=62°
21. A=49°, B=59°, C=72° 23. A=35°, B=48°, C=97°

17. Pg. 899, even
10. SAS, A=20° 12. SSS, A=48° 14. SAS, a= SAS, c= SSA, c= DNE 22. A=47°, B=59°, C=74°
24. A=46°, B=56°, C=78°

19. Pg. 899, all
19. A=44°, B=74°, C=62° 20. DNE 21. A=49°, B=59°, C=72° 22. A=47°, B=59°, C=74°
23. A=35°, B=48°, C=97° 24. A=46°, B=56°, C=78°

20. Assignment Page 900, #’s 25-42 ALL This will be checked in 45 minutes
Quiz tomorrow over 14.2!!

21. Do Now
Page 901, #’s 49 and 50

22. Pg. 900 #’s Odd
25. SSS, A=79°, B=55°, C=46° 27. SAS, b=49.1, A=110°, C=48° 29.SAS, b=3.2, A=39°, C=111° 31. SSS, DNE 33. SAS, c=6.2, A=78°, B=42°
35. SSS, A=94°, B=30°, C=56° 37. SSA, B=43°, C=79°, c= SSS, DNE 41. SSS, A=52°, B=69°, C=59°

24. Assignment
Pg. 900 #’s EVEN QUIZ Tomorrow!

25. Pg. 900, #’s Even
26. SSS, A=29°, B=105°, C= SAS, a=160, B=45°, C=21° 30. SAS, b=3.6, A=36°, C=99° 32. SSS, DNE 34. SAS, c=6.8, A=17°, B=133°
36. SSS, A=76°, B=58°, C=46° 38. SSA, B=63°, C=75°, c= SSS, DNE 42. SSS, A=74°, B=56°, C=50°

26. Pg. 986, 14.2, #’s 1-17 Odd SAS, a = 93.4 SAS, b = 12.3 SAS, a = 100.6
A=59°, B=84°, C=37°
A=39°, B=48°, C=93°
11. A=24°, B=31°, C=125°
SSS; A=48°, B=56°, C=76°
SSA; A=51°, B=57°, c=8.9
17. DNE

27. Assignment
Pg. 986, 14.2, 2-18 Even
Worksheet

28. Pg. 986, 14.2, #’s 2-18 Even SAS; c=9.3 SAS; a=35.4 SAS; c=9.1
8. A=40°, B=106, C=34°
10. A=52°, B=47°, C=81°
12. A=22°, B=27°, C=131°
SSA, DNE
16. SAS; c=83.5, A=69°, B=61°
18. SSA, a=6.4, C=92°, B=18°