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?

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.

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

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

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.

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

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!!

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

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

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

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

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

Homework Pg. 891, #’s 24-43 all

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

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

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

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

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

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

Pg. 985, 14.1, 1-14 all 144.5 in² 16.6 m² 94 cm² 8.7 in² b=8.7 c=54.1 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

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.