Law of Cosines

MM4A6c:

Apply the law of sines and the law of cosines.

Essential Question:

How do I solve problems using the Law of Cosines?

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.

Law of Cosines

Cababc

Baccab

Abccba

cos2

cos2

cos2

222

222

222

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.

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.

Example 1

a=123, c=97, B=22°, find b

Example 2

a=11.3, b=7.2, c=14.8, find A

Example 3

c=5.1, B=81°, a=4.7

Solve the triangle using the Law of Cosines and the Law of Sines

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.

Homework/Class work

Page 899 9-24 all

When possible, start with the biggest angle or side length

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*

Do Now #2

Solve the triangle:

a=8, b=12.1, c=9.4

Pg. 899, 9-23 ODD

9. 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°

Pg. 899, 10-24 even

10. SAS, A=20°

12. SSS, A=48°

14. SAS, a=8.6

16. SAS, c=64

18. SSA, c=5.3

20. DNE

22. A=47°, B=59°, C=74°

24. A=46°, B=56°, C=78°

Pg. 899, 19-24 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°

Assignment

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

Do Now

Page 901, #’s 49 and 50

Pg. 900 #’s 25-41 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=11.6

39. SSS, DNE

41. SSS, A=52°, B=69°, C=59°

Assignment

Pg. 900 #’s 26-42 EVEN

QUIZ Tomorrow!

Pg. 900, #’s 26-42 Even

26. SSS, A=29°, B=105°, C=46

28. 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=13

40. SSS, DNE

42. SSS, A=74°, B=56°, C=50°

Pg. 986, 14.2, #’s 1-17 Odd

1. SAS, a = 93.4

3. SAS, b = 12.3

5. SAS, a = 100.6

7. A=59°, B=84°, C=37°

9. A=39°, B=48°, C=93°

11. A=24°, B=31°, C=125°

13.SSS; A=48°, B=56°, C=76°

15.SSA; A=51°, B=57°, c=8.9

17. DNE

Assignment

• Pg. 986, 14.2, 2-18 Even• Worksheet

Pg. 986, 14.2, #’s 2-18 Even

2. SAS; c=9.3

4. SAS; a=35.4

6. 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°

14.SSA, DNE

16. SAS; c=83.5, A=69°, B=61°

18. SSA, a=6.4, C=92°, B=18°