Download Answers for the lesson “Apply the Sine and Cosine Ratios”

LESSON
7.6
Answers for the lesson “Apply the Sine and
Cosine Ratios”
}
Skill Practice
1. the opposite leg, the hypotenuse
2. The adjacent side is the side that
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forms part of the angle and is not
opposite the right angle; the
hypotenuse is the side opposite
the right angle.
}
Ï2 Ï2
16. }, }
2 2
17. The triangle must be a right
triangle, and you need either
an acute angle measure and the
length of one side or the lengths
of two sides of the triangle.
18. C
19. 3.0
3
4
3. } or 0.8, } or 0.6
5
5
20. 13.8
21. 20.2
35
12
4. } or 0.9459, } or 0.3243
37
37
Ï3
1
22. 7; } or 0.5, } or 0.8660
2
2
28
45
5. } or 0.5283, } or 0.8491
53
53
2Ï 2
1
23. 12; } or 0.9428, } or 0.3333
3
3
6. The ratio for sine is opposite over
hypotenuse, not adjacent over
35
12
24. 37; } or 0.3243, } or 0.9459
37
37
12
.
hypotenuse; sin A 5 }
13
Ï5
2Ï 5
25. 3; } or 0.4472, } or 0.8944
5
5
}
}
}
}
3
4
7. } or 0.6, } or 0.8
5
5
8
15
26. 34; } or 0.4706, } or 0.8824
17
17
15
8
8. } or 0.8824, } or 0.4706
17
17
56
33
27. 33; } or 0.8615, } or 0.5077
65
65
}
Ï3
1
9. } or 0.5, } or 0.8660
2
2
10. x 5 9.5, y 5 15.3
11. a 5 14.9, b 5 11.1
28. Sample answer: You can
use sin21, cos21, or tan21
to determine the angle
measure when you have the
appropriate ratio.
12. v 5 5.3, w 5 1.7
29. D
13. r 5 19.0, s 5 17.7
30. about 14 cm
14. p 5 30.6, q 5 14.9
31. about 13 cm
15. m 5 6.7, n 5 10.4
Geometry
Answer Transparencies for Checking Homework
215
32. a. A
35. a.
20 ft
x
r
41
C
y
B
y
sin A 5 }r l y 5 r sin A
x
cos A 5 }r l x 5 r cos A
y
sin A
tan A 5 }x 5 }
cos A
x 2 1 y2 5 r 2
b.
(r cos A)2 1 (r sin A)2 5 r 2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
r 2 cos 2 A 1 r 2 sin 2 A 5 r 2
r 2(cos 2A 1 sin 2 A) 5 r 2
cos 2A 1 sin 2 A 5 1
b. About 18.1 ft; the height that
the spool is off the ground has
to be added.
36. a. about 35.7 ft
b. yes
c. cosine
h
37. sin C 5 }
a , so h 5 sin C, and
1
1
Area 5 }2 bh 5 }2 b (a sin C) 5
1
} ab sin C; about 9 square units
2
38. yes
Problem Solving
33. about 36.9 ft
34. 16 ft
Geometry
Answer Transparencies for Checking Homework
216
39. a.
40. The Pythagorean Theorem tells
angle of n
depression
}
us that GT}5 Ï3 , so
Ï3
30 ft
b.
n (degrees)
40
50
equilateral, all angles must be 608.
To determine the height, drop an
altitude from one angle down; this
bisects the angle and you have a
308-608-908} triangle with
Ï3
sin E 5 }
. Therefore
2
60
sin E 5 cos G.
46.7 39.2 34.6
* (feet)
cos G 5 }
. Since n EQU is
2
41. a.
n (degrees)
70
80
31.9 30.5
* (feet)
40
Feet
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
c.
30
20
10
0
0
20
40
60
Degrees
d. Sample answer: 60 ft
80
n
u
sin u
cos u
178
0.2924
0.9563
308
0.5
0.8660
348
0.5592
0.8290
458
0.7071
0.7071
568
0.8290
0.5592
608
0.8660
0.5
738
0.9563
0.2924
908
1
0
b. For complementary angles,
the sine and cosine values are
reversed, i.e. sin 308 5 cos 608.
c. If A and B are complementary,
then sin A 5 cos B.
d. Check students’ work.
Geometry
Answer Transparencies for Checking Homework
217