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

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 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 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

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

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°