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Merrill pg. 765, 10-18

Merrill pg. 765, 10-18. 10. 24 feet 11. 251.7 meters 12. 2202.7 feet 13. 61.1 meters 14. 22.1 meters 15. 10° 16. 1° 17. 23°. 18. x=63°, y=27°, z=63°. The Law of Sines. Section 14.1 MM4A6 & MM4A7. Essential Question. How do I solve problems using the Law of Sines?.

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Merrill pg. 765, 10-18

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  1. Merrill pg. 765, 10-18 10. 24 feet 11. 251.7 meters 12. 2202.7 feet 13. 61.1 meters 14. 22.1 meters 15. 10° 16. 1° 17. 23° 18. x=63°, y=27°, z=63°

  2. The Law of Sines Section 14.1 MM4A6 & MM4A7

  3. Essential Question How do I solve problems using the Law of Sines?

  4. Important information: • To find the area of a triangle using the sine function multiply one-half by the product of two sides and the sine of the included angle. • K = ½ (side)(side)(Sin of included angle) • Law of Sines: the ratio of the sine of an angle to its opposite side is the same for all angles in a triangle.

  5. For ABC, the law of sines states the following:

  6. Example 1 • Find the area of ∆RST to the nearest tenth of a square unit.

  7. Example 2 Find the area of ∆JKL to the nearest tenth of a square unit if m<K=59°, m<L=88°, side k=6.7in, and side l=8in.

  8. Example 3 Find the area of ∆XYZ to the nearest tenth of a square unit.

  9. Assignment • Page 891, 10-23 ALL (make the angle in #22 B instead of C) • Using given information, ROUND all angles to the nearest WHOLE NUMBER before you work the problem!!

  10. Do Now • Find the area of ∆ABC, m<A=51°, m<B=62°, side a=7 in., and side c=5.2

  11. Pg. 891, 10-23 all • 14.1 in.² • 30 ft² • 42.9 in.² • 24.7 cm² • 25.2 km² • 368.2 ft² • 97.7 in.² • 160.3 m² 18. 74.2 ft² 19. 19.9 cm² 20. 20.7 km² 21. 1756.2 ft² 22. 13.7m² 23. 722.5 ft²

  12. Example 4 Use the Law of Sines to find a & b.

  13. Example 5 Solve ∆ PQR given the m<Q=115°, m<P=32°, and side p=5.6

  14. Pg. 891, 24-29 • 8.6 • 8.3 • 13.8 • 9.6 • 15.8 • 17.1

  15. Homework Pg. 891, #’s 24-43 all

  16. Do Now • Find the area of ∆ABC, m<A=57°, m<B=68°, side a=5.6 in., and side c=7.1 • Solve ∆ XYZ given the m<Y=119°, m<X=47°, and side x=6.5

  17. Pg. 891, 29-43 ODD 25. c = 8.3 27. a = 9.6 • c = 17.1 31. A=101, b=3.5, a=7.5 33. C=83, b=12.3, c=13.8 35. A=80, b=10, c=3.5 37. A=97, a=20.8, c=15.5 39. B=101, a=12.3, c=13.6

  18. Continued… 41. A=80, a=13.2, b=11.4 43. B=112, a=8.4, c=4.6

  19. Pg. 891, 24-42 even 24. b = 8.6 26. b = 13.8 28. a = 15.8 30. C=85, a=17.3, c=25.3 32. B=100, b=28.8, c=25.3 34. C=95, a=5.9, b=13.3 36. C=80, b=7.4, c=11.4

  20. Continued… 38. A=80, a=12.3, c=10.8 40. C=95, a=10.3, b=11.4 42. A=105, b=4.7, c=6.6

  21. Info… • Quiz tomorrow over 14.1: finding the area of a triangle and solving triangles using the Law of Sines • Today, do page 985, 14.1, 1-14 • Worksheet

  22. Pg. 985, 14.1, 1-14 all • 144.5 in² • 16.6 m² • 94 cm² • 8.7 in² • b=8.7 • c=54.1 • c=7.6 • b=15.6 9. B=95, a=8.2, c=3.1 10. A=123, b=16.3, c=28.7 11. B=55, a=4.4, c=11.8 12. A=98, b=27.1, c=18.7 13. B=86, b=15.6, c=10.9 14. B=45, a=19.2, c=19.9

  23. Workbook pg. 88, 1-12 • 25.5 • 24.8 • 16.7 • 29.7 • 5.6 • 28.9 • C=38, b=4.4, c=3.1 • A=35, c=21.7, a=12.7 9. C=45, a=25.8, c=18.5 10. B=44, a=5.5, b=4.0 11. C=82, a=15.5, c=21.4 12. A=75, a=82.9, c=78.4 16. 1532.7 ft.

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