Chapter 11 Answers
Alternative Activity 11-1
Reteaching 11-5
1. Check students’ work. 2. Check students’ work.
TS
3. CB
AB 5 RS 5 0.36. 4. All students have the same constant
ratio. 5. tan 20° 5 0.3639702 6. Results obtained by
drawing/measuring and by using a calculator will agree.
The calculator will display more decimal places. 7. By the
AA Similarity Postulate, any two right triangles with acute
angle A are similar. Therefore, since corresponding sides of
similar triangles are proportional, the ratio of the length of
the side opposite angle A to the length of the side adjacent to
angle A will be the same for any right triangle.
1. 12.8 mi/h at 51.3° off directly across 2a. 10 mi/h
2b. 36.9° west of due north 3. The bird’s path shifts 31.0°
east of due south 4. 4 mi/h
Alternative Activity 11-2
1. Check students’ work. 2. m/A 5 25, m/C 5 65, sin
A 5 cos C 5 0.42, cos A 5 sin C 5 0.91 3. Answers may
vary. Sample: the side opposite A is adjacent to C; the side
opposite C is adjacent to A. 4. Answers may vary. Sample:
all right triangles containing a 25° angle are similar. Therefore
corresponding sides are proportional. 5. Table values change
but it remains true that sin A 5 cos C and cos A 5 sin C.
6. No; since the length of a leg is less than the length of a
hypotenuse in a right triangle, the ratio of leg to hypotenuse
must be less than 1.
1. 19.3 in.2 2. 123.1 cm2 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 5 s 2
Practice 11-1: Example Exercises
1. tan X 5 1; tan Y 5 1 2. tan G 5 12 ; tan T 5 2
7 ; tan Q 5 24 4. tan B 5 5 ; tan C 5 12
3. tan P 5 24
7
12
5
5. tan D 5 34 ; tan E 5 43 6. tan R 5 2; tan S 5 12
7. 5.7 cm 8. 14.0 ft 9. 5.3 yd 10. 24.0 m 11. 25.7 in.
12. 6.4 km 13. 63.4 14. 36.9 15. 71.6 16. 26.6 17. 76.0
18. 33.7
Practice 11-1: Mixed Exercises
1. tan E 5 34 ; tan F 5 43 2. tan E 5 1; tan F 5 1
3. tan E 5 25 ; tan F 5 52 4. 12.4 5. 31.0 6. 14.1 7. 7.1
Alternative Activity 11-6
8. 2.3 9. 6.4 10. 78.7 11. 26.6 12. 71.6 13. 39 14. 72
1-2. Check students’ work. 3. The formula corresponds to
the formula for the area of a triangle. 4. The term CD is
CD . 5. CD 5 sin A 6. In nABC,
rewritten here as AC • AC
AC
area 5 12 (AB)(AC) sin A 7. 5018.5 ft2
15. 27 16. 68 17. 39 18. 54
Reteaching 11-1
1. 26.6 2. 76.0 3. 80.5 4. 26.6 5. 8.1
6. 89.2 7. m/A 5 53.1; m/B 5 36.9
8. m/A 5 67.4; m/B 5 22.6 9. m/A 5 70.5;
m/B 5 19.5 10. m/A 5 63.4; m/B 5 26.6 11. 49.4
© Prentice-Hall, Inc.
Reteaching 11-6
Reteaching 11-2
1. DF 5 2.7, EF 5 7.5 2. XZ 5 8.7, YZ 5 10 3. RS 5 8.4,
ST 5 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. Ï51
Reteaching 11-3
1. 42.9 ft 2. 1113.8 ft 3. 2.2° 4. 42.0 ft 5. 76.1 ft
6. 19.1 ft
Reteaching 11-4
Practice 11-2: Example Exercises
24 6. 7 7. 7 8. 24 9. 11.5
1. 54 2. 53 3. 53 4. 54 5. 25
25
25
25
10. 11.0 11. 16.5 12. 11.1 13. 7.8 14. 6.4 15. 48.6
16. 41.1 17. 30 18. 38.9 19. 26.8 20. 38.7
Practice 11-2: Mixed Exercises
3
4
3
1. sin P 5 2Ï10
7 ; cos P 5 7 2. sin P 5 5 ; cos P 5 5
5
5
Ï11
3. sin P 5 12
13 ; cos P 5 13 4. sin P 5 6 ; cos P 5 6
15
8
Ï2
5. sin P 5 Ï2
2 ; cos P 5 2 6. sin P 5 17 ; cos P 5 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 11-3: Example Exercises
1a. angle of depression from top of B to top of A 1b. angle
of elevation from top of A to top of B 1c. angle of depression
from top of A to bottom of B 1d. angle of elevation from
bottom of B to top of A 2. 66.4 ft 3. 1227.8 ft 4. 155.6 ft
5. 77.8 ft
1. k21.2, 21.2l 2. k1.9, 3.5l 3. k264.3, 76.6l 4. k5.0, 26.2l
5. k214, 0l 6. k219.9, 244.8l 7. k39.8, 4.2l 8. k20.6, 1.9l
Geometry Chapter 11
Right Triangle Trigonometry
41
Chapter 11 Answers
(continued)
5. Answers may vary. Sample:
6a. Answers may vary. Sample:
N
308
495
W
E
258
5
S
6b. 1171 ft
Practice 11-3: Mixed Exercises
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.
6. 63.4° north of east 7. 33.7° east of south 8. 45° north of
west 9. No; no magnitude given 10. Yes; magnitude and
direction given 11. No; no direction given 12. 38.6 mi/h;
31.2° north of east 13. 134.5 m; 42.0° south of west
14. 1.3 m/s; 38.7° south of east
Practice 11-5: Example Exercises
1. k21, 4l 2. k7, 6l 3. k9, 1l 4. k21, 9l 5. k1, 0l
6. k211, 21l 7. k21, 21l 8. k25, 7l 9. k2, 22l
10. x 5 30; y 5 26.0 mi/h 11. x 5 21.8; y 5 21.5 mi/h
12. x 5 61.0; y 5 19.4 mi/h 13. x 5 14.5; y 5 484.1 km
14. x 5 56.3; y 5 144.2 yd 15. x 5 48.6; y 5 1322.9 mi
16. x 5 45; y 5 35.4 lb/in.2 17. x 5 23.6; y 5 4.6 kg/cm2
18. x 5 31.0; y 5 174.9 kg/m2
Practice 11-5: Mixed Exercises
1. k1, 5l 2. k1, 21l 3. k27, 21l 4. k8, 8l 5. k1, 1l
6. k0, 8l
N
7.
358
30 ft
9b. 26 ft
W
Practice 11-4: Example Exercises
S
8.
N
Practice 11-4: Mixed Exercises
W
© Prentice-Hall, Inc.
1. k87.5, 48.5l 2. k39.7, 263.6l 3. k33.3, 47.5l
4. k74.6, 250.3l 5. k239.0, 222.5l 6. k260.9, 254.9l
7. 50.6; 37.8° south of east 8. 41.4; 52.9° north of west
9. 36.4; 15.9° west of south 10. 60; 36.9° south of east
11. 21.6; 56.3° south of west 12. 46.5; 25.5° north of east
E
E
1. k46.0, 46.0l 2. k237.1, 219.7l 3. k89.2, 280.3l
4. Answers may vary. Sample:
N
W
488
E
N
W
E
S
S
42
S
9.
10. 40; 30° west of north 11. 10; 70° north of east 12. 141;
due west 13. k3, 13l 14. k27, 25l 15. k0, 212l
Right Triangle Trigonometry
Geometry Chapter 11
Chapter 11 Answers
(continued)
16. x 5 23.6; y 5 22.9 mi/h 17. x 5 33.7; y 5 180.3 km
18. x 5 16.1; y 5 86.5 km/h
15. k92.9, 83.6l 16. k120.4, 2258.3l 17. < 211.9 mi;
< 19° south of west 18. k11, 0l 19. k4, 3l
20. Answers may vary. Sample:
y
Practice 11-6: Example Exercises
1. 124.7 cm2 2. 162.4 ft2 3. 232.5 in.2 4. 32.5 cm2
5. 259.8 in.2 6. 229.1 ft2 7. 50 ft2 8. 86.6 ft2 9. 70.7 ft2
10. 12.6 ft2 11. 24.3 m2 12. 21.0 in.2 13. 24.7 mm2
14. 129.9 mi2 15. 92.2 ft2
4
2
24 22
22
24
Practice 11-6: Mixed Exercise
1. 174.8 cm2 2. 578 ft2 3. 1250.5 mm2 4. 192.6 m2
5. 1131.4 in.2 6. 419.2 cm2 7. 324.9 in.2 8. 162 cm2
9. 37.6 m2 10. 30.1 mi2 11. 55.4 km2 12. 357.6 in.2
13. 9.7 mm2 14. 384.0 in.2 15. 54.5 cm2 16. 9.1 ft2
17. 80.9 m2 18. 83.1 m2 19. 65.0 ft2 20. 119.3 ft2
21. 8 m2 22. 55.4 ft2
Checkpoint 1
1. E 2. < 41 ft 3. < 5339 ft 4. 21.5 5. 70 6. 15
4 x
2
21. 18.8 cm2 22. 19.1 in.2 23. 268.4 ft2 24. 166.3 in.2
25. 172.0 cm2
Chapter Assessment, Form B
17
6Ï2
14
1. sin T 5 6Ï2
19 ; cos T 5 19 ; tan T 5 17 2. sin T 5 17 ;
14Ï93 3. 60 4. 19.2 5. 15.3
cos T 5 Ï93
17 ; tan T 5 93
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
Checkpoint 2
11b. angle of elevation from the person in the castle to the
1. e : 5, 53.1° north of west; f : 5.4, 68° south of west
2. k25, 21l 3. 604 mi/h; 6.7° west of north
4. Answers may vary. Sample: k3, 5l and k22, 3l
cloud 11c. angle of depression from the person in the castle
y
to the person on the ground 11d. angle of elevation from
the person on the ground to the person in the castle
12. < 46.6 ft 13. < 1710 ft
4
opposite
14. sin x ° 5 hypotenuse and
24 22
22
2
X
x8
adjacent
4 x
cos x° 5 hypotenuse
y8
24
Z
Y
opposite
opposite
hypotenuse
sin x °
cos x ° 5 hypotenuse 5 hypotenuse • adjacent
Chapter Assessment, Form A
© Prentice-Hall, Inc.
19
2Ï42
3
1. sin A 5 2Ï42
23 ; cos A 5 23 ; tan A 5 19 2. sin A 5 4 ;
3Ï7
cos A 5 Ï7
4 ; tan A 5 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
Y
14. Answers may vary. Sample:
The side opposite /X is the same
x8
as the side adjacent to /Y. The side
adjacent to /X is the side opposite
y8
/Y.
Z
X
opposite /X
adjacent /Y
So, tan x° 5 adjacent /X 5 opposite /Y 5 tan1 y °
adjacent
hypotenuse
opposite
5 adjacent 5 tan x °
15. k292.3, 59.9l 16. k371.6, 2173.3l 17. < 18.0 mi;
< 33.7° north of east 18. k1, 10l 19. k21, 3l
20. Answers may vary. Sample:
y
4
24
22
2
4 x
24
21. 72.7 in.2 22. 42.2 cm2 23. 55.4 cm2 24. 70.7 ft2
25. 688.2 m2
Geometry Chapter 11
Right Triangle Trigonometry
43
Chapter 11 Answers
(continued)
Alternative Assessment
Task 1
x 5 57.3
Scoring guide
3 Student gives correct answer and shows valid method.
2 Student gives generally correct work that contains minor
errors.
1 Student gives incorrect answer and method is not correct.
0 Student makes little or no effort.
18. D 19. Answers may vary. Sample: You can prove a
quadrilateral is a parallelogram by proving opposite sides congruent, opposite angles congruent, or one pair of opposite
sides congruent and parallel. 20. Check students’ work.
21. Answers may vary. Sample:
22. 133 ft
Standardized Test Practice
Task 2
242 ft
Scoring guide
3 Student gives correct answer and shows valid method.
2 Student gives generally correct work that contains minor
errors.
1 Student gives incorrect answer and method is not correct.
0 Student makes little or no effort.
Task 3
a. a: k12, 23l; b: k8, 8l b. a: 12.4; b: 11.3 c. a: < 14° south
of east; b: 45° north of east
1. A 2. C 3. D 4. B 5. B 6. D 7. C 8. A 9. A 10. B
11. E 12. A 13. B 14. B 15. C 16. D 17. A 18. B
19. D
20. c # 3
25 24 23 22 21 0 1
3
4
5
21. x 5 57; y 5 44; z 5 79
22. Answers may vary. Sample:
X
W
S
Y
Z
Scoring Guide
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.
2
V
T
U
5 25. 343 26. Check students’ work.
23. C(r 1 s, t) 24. 26
729
Task 4
208.7 cm2
© Prentice-Hall, Inc.
Scoring guide
3 Student gives correct answer and shows valid method.
2 Student gives generally correct work that contains minor
errors.
1 Student gives incorrect answer and method is not correct.
0 Student makes little or no effort.
Cumulative Review
1. D 2. C 3. D 4. D 5. B 6. C 7. A 8. A 9. A
10. B 11. B 12. C 13. B 14. B 15. D 16. D 17. B
44
Right Triangle Trigonometry
Geometry Chapter 11