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:

SinA SinB SinC

a b c

A

a

B

bC

c

Example 1

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

96

60 24R

S

T

7.6r

7.7s

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.

X

YZ80 28

4.8z0.4y

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

1. 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

10.14.1 in.²

11. 30 ft²

12. 42.9 in.²

13. 24.7 cm²

14. 25.2 km²

15. 368.2 ft²

16. 97.7 in.²

17. 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

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

24. 8.6

25. 8.3

26. 13.8

27. 9.6

28. 15.8

29. 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

29.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

1. 144.5 in²

2. 16.6 m²

3. 94 cm²

4. 8.7 in²

5. b=8.7

6. c=54.1

7. c=7.6

8. 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

Workbook pg. 88, 1-12

1. 25.5

2. 24.8

3. 16.7

4. 29.7

5. 5.6

6. 28.9

7. C=38, b=4.4, c=3.1

8. 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.