Chapter 9 Answers (continued)

Chapter 9 Answers
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Practice 9-1
3
4
1. tan E = 4; tan F = 3
2. tan E = 1; tan F = 1
2
5
3. tan E = 5; tan F = 2
4. 12.4 5. 31.0 6. 14.1
7. 7.1 8. 2.3 9. 6.4 10. 78.7 11. 26.6
12. 71.6 13. 39 14. 72 15. 27 16. 68
17. 39 18. 54
Practice 9-2
2"10
3
4 3
1. sin P = 7 ;cosP = 7 2. sin P = 5 ;cosP = 5
12
5
"11
5
3. sin P = 13;cosP = 13
4. sin P = 6 ;cosP = 6
"2
"2
15
8
5. sin P = 2 ;cosP = 2
6. sin P = 17;cosP = 17
7. 64 8. 11.0 9. 7.0 10. 42 11. 7.8 12. 53
13. 6.6 14. 37 15. 11.0 16. 56 17. 11.5
18. 9.8
Practice 9-3
1a. angle of depression from the birds to the ship
1b. angle of elevation from the ship to the birds
1c. angle of depression from the ship to the submarine
1d. angle of elevation from the submarine to the ship
2a. angle of depression from the plane to the person
2b. angle of elevation from the person to the plane
2c. angle of depression from the person to the sailboat
2d. angle of elevation from the sailboat to the person
3. 116.6 ft 4. 84.8 ft 5. 46.7 ft 6. 31.2 yd
7. 127.8 m 8. 323.6 m
9a.
9b. 26 ft
35
30 ft
Practice 9-4
1. 46.0, 46.0 2. -37.1, -19.7 3. 89.2, -80.3
4. 38.6 mi/h; 31.2º north of east 5. 134.5 m; 42.0º south
of west 6. 1.3 m/sec; 38.7º south of east 7. 55º north
of east 8. 20º west of south 9. 33º west of north
10a. 1, 5 10b.
y
6
4
642 2 4 6 x
2
4
6
11a. 1, -1 11b.
12a. -7, -1 12b.
13. Sample:
N
W
14. Sample:
N
W
30
S
S
48
y
6
4
642 4 6 x
2
E
E
4
6
Practice 9-5
1. 174.8 cm 2 2. 578 ft 2 3. 1250.5 mm 2
4. 192.6 m 2 5. 1131.4 in. 2 6. 419.2 cm 2
7. 324.9 in. 2 8. 162 cm 2 9. 37.6 m 2 10. 30.1 mi 2
11. 55.4 km 2 12. 357.6 in. 2 13. 9.7 mm 2
14. 384.0 in. 2 15. 54.5 cm 2 16. 9.1 ft 2
17. 80.9 m 2 18. 83.1 m 2 19. 65.0 ft 2 20. 119.3 ft 2
21. 8 m 2 22. 55.4 ft 2
Reteaching 9-1
1. 26.6 2. 76.0 3. 80.5 4. 26.6
5. 8.1 6. 0.8 7. mA = 53.1; mB = 36.9
8. mA = 67.4; mB = 22.6 9. mA = 70.5;
mB = 19.5 10. mA = 63.4; mB = 26.6
11. 26.6 12. 63.4 13. 49.4
6
4
2
y
42
2 4 6 x
4
6
Geometry Chapter 9 Answers 29

Chapter 9 Answers (continued)
Reteaching 9-2
1. DF = 2.7, EF = 7.5 2. XZ = 8.7, YZ = 10
3. RS = 8.4, ST = 13.1 4. 5.8 5. 30; 60 6. 16.6;
73.4 7. 23.6; 66.4 8. 2.1; 3.4 9a. 7.1 9b. "51
Reteaching 9-3
1. 42.9 ft 2. 1113.8 ft 3. 2.2° 4. 42.0 ft
5. 76.1 ft 6. 19.1 ft
Reteaching 9-4
1. 12.8 mi/h at 51.3° off directly across 2a. 10 mi
2b. 36.9° west of due north 3. The bird’s path shifts 31.0°
east of due south. 4. 4 mi/h
Reteaching 9-5
1. 19.3 in. 2 2. 123.1 cm 2 3. 86.6 in. 2 4. 172.0 in. 2
5. 363.3 in. 2 6. 126.3 in. 2 7a. 81 in. 2 7b. area of
square = s 2
Enrichment 9-1
1. 3 2. –2 3. 45° 4. 135°; definition of
supplementary angles 5. 45°; vertical angles are
congruent. 6. 135°; vertical angles are congruent.
7.
y
y 2x 3
x 2y 4
1
8. -2, 2
9. 90°, 90° 10. No; because the slopes of the
lines are opposite reciprocals, the lines must be perpendicular.
11. 70.6°, 109.4°
Enrichment 9-2
1. 5.8 cm 2. 3.4 cm 3. 7.5 cm 4. 47 5. 25.5
6. 107.5 7. 0.731 8. 0.431 9. 0.951 10. 7.9
11. 7.9 12. 7.9 13. They are equal. 14. The sides
of a triangle are proportional to the sides of their opposite
angles. 15. 70 16. 15.55 km 17. 11.83 km
18. Lighthouse Q; it is closer.
x
Enrichment 9-3
1. the top of the tower 2.
3.
4. the angle of elevation from B to the top of the tower;
30°-60°-90°; scalene right triangle 5. the angle of elevation
from A to the top of the tower; 45°-45°-90°; isosceles right
x x
triangle 6. tan 60 = y 7. tan 45 = y 1 100
8. x = tan 60(y); x = tan 45(y + 100) 9. 136.6
10. 236.6; the height of the tower 11. yes
Enrichment 9-4
1. (0.5, 0.5) 2. (-0.25, 1.80) 3. (-2.25, 1.80)
4. 2.9 km; 38.7° south of east
Enrichment 9-5
1. 36 cm 2 2. 4"3
cm or about 6.93 cm 3. 6 cm
4. A = 6 sin u, 0° u 180°
Chapter Project
Activity 1: Building
1 and 2 are complementary, and 2 and 3 are
complementary, so m1 = m3.
line of sight
3
string
2
P
60 45
B y M A y 100 M
horizon
line
edge
of
protractor
Activity 2: Measuring
Check students’ work.
Activity 3: Comparing
Check students’ work.
Activity 4: Researching
Check students’ work.
1
x
✔ Checkpoint Quiz 1
PM
P
4
4
3
3
3
1. tan A = 3, sin A = 5,cosA = 5; tan B = 4, sin B = 5,
4
cos B = 5
2. tan A = 2, sin A = 0.8955, cos A = 0.4478;
tan B = 0.5, sin B = 0.4478, cos B = 0.8955
3. tan A = 0.8833, sin A = 0.6625, cos A = 0.75;
tan B = 1.1321, sin B = 0.75, cos B = 0.6625 4. 11.6
5. 41° 6. 16.5 7. 22.5 ft
x
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30
Answers Geometry Chapter 9

Chapter 9 Answers (continued)
© Pearson Education, Inc. All rights reserved.
✔ Checkpoint Quiz 2
1. (71, 79) 2. (16, -9) 3. (-60, 148) 4. 31.6, 71.6°
north of east 5. 16.1, 29.7° south of west 6. 120.4,
48.4° north of west 7. 119.3 ft 2 8. 293.9 m 2
9. 523.1 in. 2
Chapter Test, Form A
2"42
19
2"42
1. sin A = 23 ;cosA = 23; tan A = 19
3 "7
3"7
2. sin A = 4 ;cosA = 4 ; tan A = 7 3. 67
4. 20.9 5. 13.4 6. 27 7. 76.0 8. 26.6
9. 36.9 10. 71.6 11a. angle of elevation from the
person to the top of the tree 11b. angle of depression
from the top of the tree to the person 11c. angle of
elevation from the top of the tree to the birds 11d. angle
of depression from the birds to the top of
the tree 12. 102 ft 13. 143 ft X
14. Sample: The side opposite X is the
same as the side adjacent to Y.The side
x
adjacent to X is the same as the side
y
opposite Y.
Z Y
opposite /X adjacent /Y 1
So, tan x° = adjacent /X = opposite /Y = tan y8.
15. 92.9, 83.6 16. 120.4, -258.3 17. 211.9 mi;
19° south of west 18. 11, 0 19. 4, 3
20. Sample:
y
4
2
4 2
2
2 4
4
21. 18.8 cm 2 22. 19.1 in. 2 23. 268.4 ft 2
24. 166.3 in. 2 25. 172.0 cm 2
Chapter Test, Form B
x
6"2
17
6"2
1. sin T = 19 ;cosT = 19; tan T = 17
14
"93
14"93
2. sin T = 17;cosT = 17 ; tan T = 93
3. 60
4. 19.2 5. 15.3 6. 63 7. 63.4 8. 26.6
9. 36.9 10. 78.7 11a. angle of depression from the cloud
to the person in the castle 11b. angle of elevation from the
person in the castle to the cloud 11c. angle of depression
from the person in the castle to the person on the ground
11d. angle of elevation from the person on the ground to
the castle 12. 46.6 ft 13. 1710 ft
opposite
adjacent X
14. sin x° = hypotenuse and cos x° = hypotenuse
sin x8 opposite adjacent
cos x8 = hypotenuse hypotenuse =
x
opposite hypotenuse
y
hypotenuse ? adjacent =
Z
opposite
adjacent = tan x°
15. -92.3, 59.9 16. 371.6, -173.3 17. 18.0 mi;
33.7° north of east 18. 1, 10 19. -1, 3
20. Sample:
y
4
4
2
4
2 4
x
21. 72.7 in. 2 22. 42.2 cm 2 23. 55.4 cm 2
24. 70.7 ft 2 25. 688.2 m 2
Alternative Assessment, Form C
TASK 1 Scoring Guide:
x = 57.3
3 Student gives correct answer and shows a valid method.
2 Student gives generally correct work that contains
minor errors.
1 Student gives an incorrect answer, and the method is
not correct.
0 Student makes little or no effort.
TASK 2 Scoring Guide:
111 ft
3 Student gives a correct answer and shows a valid method.
2 Student gives generally correct work that contains
minor errors.
1 Student gives an incorrect answer, and the method is
not correct.
0 Student makes little or no effort.
TASK 3 Scoring Guide:
a. W
W W 12, -3; 8, 8 b. W W W
a b a 12, 4; b 11, 3
c. a 14° south of east; b 45° north of east
3 Student gives correct answers.
2 Student gives answers that are mostly correct.
1 Student gives mostly incorrect answers.
0 Student makes little or no effort.
Y
Geometry Chapter 9 Answers 31

Chapter 9 Answers (continued)
TASK 4 Scoring Guide:
249.4 cm 2
3 Student gives correct answer and shows a valid method.
2 Student gives generally correct work that contains
minor errors.
1 Student gives an incorrect answer, and the method is
not correct.
0 Student makes little or no effort.
Cumulative Review
1. A 2. C 3. D 4. B 5. D 6. B 7. C
8. D 9. A 10. A 11. B 12. C 13. D
14. 10 15. 60 16. 190 ft 2 17. Sample: The side
opposite the 90° angle is also the hypotenuse, and there are
two adjacent sides. 18. Sample: The sum of the three
angles of a triangle is 180°. On a sphere, the sum of the three
angles will be greater than 180°.
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32
Answers Geometry Chapter 9