law of cosines mm4a6c: apply the law of sines and the law of cosines
TRANSCRIPT
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°