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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.
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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.
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°