Lesson Practice B 7walker.rigbytrojans.org/uploads/2/1/5/4/21541244/practice_7.6_and_key.pdfLesson...
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Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Practice B For use with the lesson “Apply the Sine and Cosine Ratios” Find sin R and sin S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary. 1. T S R 20 15 25 2. T S R 26 10 24 3. T S R 16 30 34 4. T S R 42 40 58 5. T S R 53 28 45 6. T S R 117 125 44 Find cos A and cos B. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary. 7. A C B 52 20 48 8. B C A 12 37 35 9. 24 18 30 A C B 10. 50 14 48 B A C 11. 73 48 55 A C B 12. 72 97 65 A C B Use a cosine or sine ratio to find the value of each variable. Round decimals to the nearest tenth. 13. 578 14 b a 14. 418 17 c d 15. 368 21 r s 16. 518 32 t u 17. 478 12 y x 18. 398 44 h g Name ——————————————————————— Date ———————————— Geometry Chapter Resource Book 7-80 LESSON 7.6 LESSON 7 .6
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Practice BFor use with the lesson “Apply the Sine and Cosine Ratios”
Find sin R and sin S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.
1.
T S
R
20
15
25
2. TS
R
2610
24 3. T
S
R
16
30
34
4. T
S R
4240
58
5. T
S
R
5328
45 6.
T
S
R117
12544
Find cos A and cos B. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.
7.
A C
B
52 20
48
8.
BC
A
1237
35
9. 24
18 30
AC
B
10. 5014
48 B
A
C
11. 73
48 55
A
C
B 12.
72
97
65
A
C
B
Use a cosine or sine ratio to find the value of each variable. Round decimals to the nearest tenth.
13. 578
14
ba
14.
418
17c
d
15. 368
21
r
s
16. 518
32
t u
17.
47812
y
x
18. 398
44
h
g
Name ——————————————————————— Date ————————————
GeometryChapter Resource Book7-80
Lesson
7.6
Les
so
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.6
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Use the 458-458-908 Triangle Theorem or the 308-608-908 Triangle Theorem to find the sine and cosine of the angle.
19. a 308 angle 20. a 458 angle 21. a 608 angle
Find the unknown side length. Then find sin A and cos A. Write each answer as a fraction in simplest form and as a decimal. Round to four decimal places, if necessary.
22.
33 56
C
B A
23.
36 85
C
B
A
24.
6
2
B
CA
7
25. 12
3
B
C
A
7
26. Ski Lift A chair lift on a ski slope has an angle
288
4640 fth
of elevation of 288 and covers a total distance of 4640 feet. To the nearest foot, what is the vertical height h covered by the chair lift?
27. Airplane Landing You are preparing to land
Not drawn to scale
38
d500 ft
Approach path an airplane. You are on a straight line approach path that forms a 38 angle with the runway. What is the distance d along this approach path to your touchdown point when you are 500 feet above the ground? Round your answer to the nearest foot.
28. Extension Ladders You are using extension ladders
75.58
to paint a chimney that is 33 feet tall. The length of an extension ladder ranges in one-foot increments from its minimum length to its maximum length. For safety, you should always use an angle of about 75.58 between the ground and the ladder.
a. Your smallest extension ladder has a maximum length of 17 feet. How high does this ladder safely reach on a vertical wall?
b. You place the base of the ladder 3 feet from the chimney. How many feet long should the ladder be?
c. To reach the top of the chimney, you need a ladder that reaches 30 feet high. How many feet long should the ladder be?
Practice B continuedFor use with the lesson “Apply the Sine and Cosine Ratios”
Name ——————————————————————— Date ————————————
GeometryChapter Resource Book 7-81
Lesson
7.6
Les
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Lesson Apply the Sine and Cosine Ratios, continued 5. about 4.7 ft 6. about 3.3 ft
Technology Activity
1. Answers will vary. 2. no; yes
3. They are approximately equal; the triangles are similar, so ratios of corresponding lengths should be equal; no 4. Yes; Sample answer: Students chose different measures for ∠ B, which resulted in different ratios.
Practice Level A
1. sin R 5 4 } 5 5 0.8, sin S 5
3 } 5 5 0.6
2. sin R 5 15
} 17
< 0.8824, sin S 5 8 }
17 < 0.4706
3. sin R 5 12
} 13
< 0.9231, sin S 5 5 }
13 < 0.3846
4. sin R 5 7 }
25 5 0.28, sin S 5
24 }
25 5 0.96
5. sin R 5 20
} 29
< 0.6897, sin S 5 21
} 29
< 0.7241
6. sin R 5 55
} 73
< 0.7534, sin S 5 48
} 73
< 0.6575
7. cos A 5 15
} 17
< 0.8824, cos B 5 8 }
17 < 0.4706
8. cos A 5 5 }
13 < 0.3846, cos B 5
12 }
13 < 0.9231
9. cos A 5 4 } 5 5 0.8, cos B 5
3 } 5 5 0.6
10. cos A 5 7 }
25 5 0.28, cos B 5
24 }
25 5 0.96
11. cos A 5 20
} 29
< 0.6897, cos B 5 21
} 29
< 0.7241
12. cos A 5 72
} 97
< 0.7423, cos B 5 65
} 97
< 0.6701
13. a < 6.4, b ø 7.7 14. c < 4.7, d < 5.2
15. e < 6.9, f < 9.8 16. g < 12.3, h < 8.6
17. j < 14.1, k < 15.6 18. m < 30.9, n < 39.7
19. sin 308 5 0.5, cos 308 5 Ï
}
3 } 2
20. sin 458 5 cos 458 5 Ï
}
2 }
2
21. sin 608 5 Ï
}
3 }
2 , cos 608 5 0.5
22. AB 5 53, sin A 5 28
} 53
< 0.5283,
cos A 5 45
} 53
< 0.8491
23. AC 5 48, sin A 5 7 }
25 5 0.28,
cos A 5 24
} 25
5 0.96
24. AB 5 40, sin A 5 3 } 5 5 0.6, cos A 5
4 } 5 5 0.8
25. BC 5 21, sin A 5 21
} 29
< 0.7241,
cos A 5 20
} 29
< 0.6897 26. 8 ft
27. v < 1,841 ft, h < 21,040 ft 28. 5.5 ft
Practice Level B
1. sin R 5 3 } 5 5 0.6, sin S 5
4 } 5 5 0.8
2. sin R 5 12
} 13
< 0.9231, sin S 5 5 }
13 < 0.3846
3. sin R 5 8 }
17 < 0.4706, sin S 5
15 }
17 < 0.8824
4. sin R 5 20
} 29
< 0.6897, sin S 5 21
} 29
< 0.7241
5. sin R 5 28
} 53
< 0.5283, sin S 5 45
} 53
< 0.8491
6. sin R 5 44
} 125
5 0.352, sin S 5 117
} 125
5 0.936
7. cos A 5 12
} 13
< 0.9231, cos B 5 5 }
13 < 0.3846
8. cos A 5 12
} 37
< 0.3243, cos B 5 35
} 37
< 0.9459
9. cos A 5 4 } 5 5 0.8, cos B 5
3 } 5 5 0.6
10. cos A 5 7 }
25 5 0.28, cos B 5
24 }
25 5 0.96
11. cos A 5 48
} 73
< 0.6575, cos B 5 55
} 73
< 0.7534
12. cos A 5 72
} 97
< 0.7423, cos B 5 65
} 97
< 0.6701
13. a < 9.1, b < 16.7 14. c < 19.6, d < 25.9
15. r < 28.9, s < 35.7 16. t < 24.9. u < 20.1
17. x < 8.2, y < 8.8 18. g < 56.6, h < 35.6
19. sin 308 5 0.5, cos 308 5 Ï
}
3 } 2
20. sin 458 5 cos 458 5 Ï
}
2 }
2
21. sin 608 5 Ï
}
3 }
2 , cos 608 5 0.5
22. AB 5 65, sin A 5 33
} 65
< 0.5077,
cos A 5 56
} 65
< 0.8615
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Lesson Apply the Sine and Cosine Ratios, continued
23. AC 5 77, sin A 5 36
} 85
< 0.4235,
cos A 5 77
} 85
< 0.9059
24. AB 5 8, sin A 5 Ï
} 7 }
4 < 0.6614,
cos A 5 3 }
4 5 0.75
25. BC 5 9, sin A 5 3 }
4 5 0.75,
cos A 5 Ï
} 7 }
4 < 0.6614
26. 2178 ft 27. about 9554 ft
28. a. about 16.5 ft b. 12 ft c. 31 ft
Practice Level C
1. sin R 5 72
} 97
< 0.7423, sin S 5 65
} 97
< 0.6701
2. sin R 5 28
} 53
< 0.5283, sin S 5 45
} 53
< 0.8491
3. sin R 5 91
} 109
< 0.8349, sin S 5 60
} 109
< 0.5505
4. cos A 5 77
} 85
< 0.9059, cos B 5 36
} 85
< 0.4235
5. cos A 5 51
} 149
< 0.3423, cos B 5 140
} 149
< 0.9396
6. cos A 5 21
} 29
< 0.7241, cos B 5 20
} 29
< 0.6897
7. a < 16.6, b < 27.5 8. c < 45.7, d < 58.8
9. e < 3.1, f < 4.3 10. g < 15.9, h < 18.8
11. j < 62.9, k < 69.9 12. m < 92.2, n < 47.5
13. 346.9 in. 14. D
15. AB 5 149, sin A 5 51
} 149
< 0.3423,
cos A 5 140
} 149
< 0.9396
16. AC 5 160, sin A 5 9 }
41 < 0.2195,
cos A 5 40
} 41
< 0.9756
17. AC 5 20, sin A 5 6 Ï
}
61 }
61 < 0.7682,
cos A 5 5 Ï
}
61 }
61 5 0.6402
18. BC 5 24, sin A 5 3 }
4 5 0.75,
cos A 5 Ï
} 7 }
4 < 0.6614
19. 321.4 m 20. b sin A 21. a sin B
22. Since h 5 b sin A and h 5 a sin B, by
substitution b sin A 5 a sin B. So sin A
} a 5
sin B }
b .
23. 386 ft apart, 270 ft tall
Study Guide
1. sin A < 0.2195; sin B < 0.9756
2. sin A < 0.8349; sin B < 0.5505
3. cos A < 0.5283; cos B < 0.8491
4. cos A < 0.5077; cos B < 0.8615
5. 8.4 6. 48.3
Interdisciplinary Application
1. about 9.78 m 2. about 79.928 3. 10.088
4. 5.28 5. about 1.678 6. 55.839 m
Challenge Practice
1. Sample answer: Since PT 5 QT, we have ∠ PQT > ∠ P, so m∠ PQT 5 368. So by the Exterior Angle Theorem, m∠ QTR 5 m∠ P 1 m∠ PQT 5 368 1 368 5 728.
Applying the Base Angles Theorem again, since QT 5 QR, we have m∠ R 5 m∠ QTR 5 728, so m∠ RQT 5 1808 2 728 2 728 5 368.
So ∠ RQT > ∠ RPQ, and ∠ R > ∠ R (Reflexive Property of Congruence); therefore, n PRQ , n QRT (AA Similarity Postulate).
2. 1 }
2x 5
1 1 2x } 1 ; x 5
21 6 Ï}
5 } 4
3. ∠ SQT (or ∠ RQS); 21 1 Ï
} 5 }
4
4. (sin a8)2 1 (cos a8)2 5 1 x } z 2 2 1 1 y } z 2
2 5
x2 1 y2
} z2 5
z2
} z2 5 1 5. 0.8
6. AB ø 36.5, BC ø 26.1
7.
a
b
c
x8
sin x8 5 a } c
In any right triangle, a ≤ c so sin x8 5 a } c ≤ 1.
8.
a
b
c
x8
cos x8 5 b } c
In any right triangle, b ≤ c so cos x8 5 b } c ≤ 1.
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Chapter Resource Book
7.6
