Name ———————————————————————
Date ————————————
Practice A
LESSON
7.6
For use with pages 491–498
1. R
2. R
10
6
T
3. S
17
8
T
S
8
4. S
5.
T
5
R
S
15
21
T
6.
R
T
55
20
R
24
T
13
25
7
12
LESSON 7.6
Find sin R and sin S. Write each answer as a fraction and as a decimal.
Round to four decimal places, if necessary.
48
29
S
R
73
S
Find cos A and cos B. Write each answer as a fraction and as a decimal.
Round to four decimal places, if necessary.
7.
B
34
8.
9.
A
12
C
A
Copyright © Holt McDougal. All rights reserved.
10.
B
11. A
A
20
B
24
C
30
A
26
10
16
16
C
58
B
12.
C
75
21
C
40
B
72
65
42
C
72
B
97
A
Use a sine or cosine ratio to find the value of each variable.
Round decimals to the nearest tenth.
13.
14.
a
508
15.
10
7
c
428
d
17.
15
18.
558
g
e
12
b
16.
f
358
h
488
j
21
m
25
398
n
k
Geometry
Chapter 7 Resource Book
55
Name ———————————————————————
Practice A
LESSON
LESSON 7.6
7.6
For use with pages 491–498
Date ————————————
continued
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.
23.
C
45
28
C
14
B
B
50
B
A
24.
A
25. A
24
29
B
20
C
A
32
C
26. Staircase A staircase has an angle of elevation of 288
and covers a total distance of 17 feet. To the nearest
foot, what is the vertical height h covered by the staircase?
17 ft
288
27. Highway You are traveling along a stretch of highway
4 mi
that has a slight grade with an angle of inclination of 5°.
After traveling for 4 miles, what is the vertical v and
horizontal h change in feet? (1 mi 5 5280 ft) Round
your answer to the nearest foot.
58
h
Not drawn to scale
28. Ladder You lean a 16 foot ladder against the wall.
If the ladder makes an angle of 70° with the ground,
how far away from the wall is the base of the ladder?
Round your answer to the nearest tenth of a foot.
16 ft
708
56
Geometry
Chapter 7 Resource Book
v
Copyright © Holt McDougal. All rights reserved.
h
Lesson 7.5, continued
}
3. True in all cases except when x 5 908 or
x 5 08; because tan 08 5 0 and tan 908 is undefined.
4.
608
2x
45
< 0.8491
cos A 5 }
53
308
7
23. AC 5 48, sin A 5 } 5 0.28,
25
x 3
1
Ï3
Using the diagram, tan 308 5 }
} and
}
24
5 0.96
cos A 5 }
25
tan 608 5 Ï 3 . If a8 5 b8 5 308,
1
Ï3
1
Ï3
2
Ï3
3
4
24. AB 5 40, sin A 5 } 5 0.6, cos A 5 } 5 0.8
5
5
tan a8 1 tan b8 5 }
} 1 }
} 1 }
} , but
}
tan(a8 1 b8) 5 tan(308 1 308) 5 tan 608 5 Ï 3 .
So, tan a8 1 tan b8 Þ tan(a8 1 b8).
5. Sketch 1 6. Sketch 2 7. Sketch 3
21
25. BC 5 21, sin A 5 } < 0.7241,
29
20
< 0.6897 26. 8 ft
cos A 5 }
29
27. v < 1,841 ft, h < 21,040 ft 28. 5.5 ft
Lesson 7.6
Copyright © Holt McDougal. All rights reserved.
28
22. AB 5 53, sin A 5 } < 0.5283,
53
ANSWERS
x
Ï3
21. sin 608 5 }, cos 608 5 0.5
2
Practice Level A
3
4
1. sin R 5 } 5 0.8, sin S 5 } 5 0.6
5
5
15
8
2. sin R 5 } < 0.8824, sin S 5 } < 0.4706
17
17
5
12
3. sin R 5 } < 0.9231, sin S 5 } < 0.3846
13
13
7
24
4. sin R 5 } 5 0.28, sin S 5 } 5 0.96
25
25
20
21
5. sin R 5 } < 0.6897, sin S 5 } < 0.7241
29
29
55
48
6. sin R 5 } < 0.7534, sin S 5 } < 0.6575
73
73
15
8
7. cos A 5 } < 0.8824, cos B 5 } < 0.4706
17
17
5
12
8. cos A 5 } < 0.3846, cos B 5 } < 0.9231
13
13
3
4
9. cos A 5 } 5 0.8, cos B 5 } 5 0.6
5
5
7
24
10. cos A 5 } 5 0.28, cos B 5 } 5 0.96
25
25
20
21
11. cos A 5 } < 0.6897, cos B 5 } < 0.7241
29
29
72
65
12. cos A 5 } < 0.7423, cos B 5 } < 0.6701
97
97
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
}
Ï3
19. sin 308 5 0.5, cos 308 5 }
2
}
Ï2
20. sin 458 5 cos 458 5 }
2
Practice Level B
3
4
1. sin R 5 } 5 0.6, sin S 5 } 5 0.8
5
5
5
12
2. sin R 5 } < 0.9231, sin S 5 } < 0.3846
13
13
8
15
3. sin R 5 } < 0.4706, sin S 5 } < 0.8824
17
17
20
21
4. sin R 5 } < 0.6897, sin S 5 } < 0.7241
29
29
28
45
5. sin R 5 } < 0.5283, sin S 5 } < 0.8491
53
53
117
44
6. sin R 5 } 5 0.352, sin S 5 } 5 0.936
125
125
5
12
7. cos A 5 } < 0.9231, cos B 5 } < 0.3846
13
13
35
12
8. cos A 5 } < 0.3243, cos B 5 } < 0.9459
37
37
3
4
9. cos A 5 } 5 0.8, cos B 5 } 5 0.6
5
5
7
24
10. cos A 5 } 5 0.28, cos B 5 } 5 0.96
25
25
48
55
11. cos A 5 } < 0.6575, cos B 5 } < 0.7534
73
73
72
65
12. cos A 5 } < 0.7423, cos B 5 } < 0.6701
97
97
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
}
Ï3
19. sin 308 5 0.5, cos 308 5 }
2
}
Ï2
20. sin 458 5 cos 458 5 }
2
Geometry
Chapter 7 Resource Book
A7