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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.
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