Name ——————————————————————— Date ————————————Co

pyrig

ht ©

Hol

t McD

ouga

l. Al

l rig

hts

rese

rved

.

GeometryChapter 7 Resource Book 71

LESSON

7.7 Practice CFor use with pages 503–509

Use a calculator to approximate the measure of ∠ A to the nearest tenth of a degree.

1.

B

A

C37

29

2.

A

B C

236

3.

C

B

A

12

60

Solve the right triangle. Round decimal answers to the nearest tenth. Check that your answer is reasonable.

4. P

R338

18

5.

P

N

7

12 6.

J

K

L

62.38

9

7.

W

V

X

178

34

8.

A C

B

25.58

17

9.

M

E

U

18

72

10.

208

132

R

T

A

11. 10.6

27.28

V M

D

12.

31.3

7.5

U

S

T

Let ∠ A be an acute angle in a right triangle. Approximate the measure of ∠ A to the nearest tenth of a degree.

13. sin A 5 0.16 14. tan A 5 1.8 15. sin A 5 0.97 16. cos A 5 0.25

17. tan A 5 8.4 18. cos A 5 0.81 19. sin A 5 0.44 20. cos A 5 0.05

21. tan A 5 1.0 22. cos A 5 0 23. sin A 5 1.0 24. sin A 5 0

LES

SO

N 7.7

LAHGE11FLCRB_c07_067-078.indd 71 2/2/09 1:09:44 PM

Name ——————————————————————— Date ————————————

Copy

right

© H

olt M

cDou

gal.

All r

ight

s re

serv

ed.

GeometryChapter 7 Resource Book72

25. Golf The angle of depression from the tee box to

Not drawn to scale

108

185 yd

the green is 108 on a par 3, 185 yard hole. How much higher is the tee box than the green? Round to the nearest yard.

26. Ramp You are designing a ramp where the

verticalriselength of ra

mp

ramp angle

horizontal distance

horizontal distance is twice as long as the vertical rise. What will be the ramp angle to the nearest tenth of a degree?

27. Bridge A surveyor needs to fi nd the distance 325 ftA B

C

428 1108BC across a lake as part of a project to build a bridge. The distance from point A to point B is 325 feet. The measurement of angle A is 428 and the measurement of angle B is 1108. What is the distance BC across the lake to the nearest foot?

In Exercises 28–30, use the following information.

Fireworks You are watching a fi reworks display where you are standing 290 feet behind the launch pad. The launch tubes are aimed directly away from you at an angle of 658 with the ground. The angle of elevation for you to see the fi reworks is 408.

290 ft408 658

A

28. To the nearest foot, what is the horizontal distance from the launch pad to the ignition point of the fi reworks?

29. To the nearest foot, what is the height of the fi reworks when they ignite?

30. What is the measure of angle A?

LESSON

7.7 Practice C continuedFor use with pages 503–509

LES

SO

N 7

.7

LAHGE11FLCRB_c07_067-078.indd 72 2/2/09 1:10:03 PM

Copy

right

© H

olt M

cDou

gal.

All r

ight

s re

serv

ed.

A9Geometry

Chapter 7 Resource Book

Focus On 7.6Practice

1. cot D 5 24

} 7 < 3.4286; sec D 5 25

} 24

< 1.0417;

csc D 5 25

} 7 < 3.5714

2. cot D 5 9 }

40 5 0.225; sec D 5

41 }

9 < 4.5556;

csc D 5 41

} 40

5 1.025

3. cot D 5 60

} 11

< 5.4545; sec D 5 61

} 60

< 1.0167;

csc D 5 61

} 11

< 5.5455

4. cot D 5 20

} 21

< 0.9524; sec D 5 29

} 20 = 1.45;

csc D 5 29

} 21

< 1.3810

5. cot D 5 72

} 65

< 1.1077; sec D 5 97

} 72

< 1.3472;

csc D 5 97

} 65

< 1.4923

6. cot D 5 80

} 39 < 2.0513; sec D 5 89

} 80

= 1.1125;

csc D 5 89

} 39 < 2.2821

7. 9.7 8. 13.5 9. 21.8

10. approximately 215.58 ft 11. 37 m

Review for Mastery

1. cot D 5 4 }

3 < 1.3333; sec D 5

5 }

4 < 1.25;

csc D 5 5 }

3 < 1.6667

2. cot D 5 36

} 77 < 0.4675; sec D 5 85

} 36

< 2.3611;

csc D 5 85

} 77 < 1.1039

3. cot D 5 48

} 55 < 0.8727; sec D 5 73

} 48

< 1.5208;

csc D 5 73

} 55 < 1.3273

4. 17.8 5. 7.0 6. 13.3

Lesson 7.7Practice Level A

1. A 2. B 3. E 4. B 5. A 6. F

7. m∠ A 5 56.38 8. m∠ A 5 53.78

9. m∠ A 5 32.68 10. m∠ A 5 51.38

11. m∠ A 5 39.58 12. m∠ A 5 65.98

13. m∠ P 5 458, PQ < 8.5, QR < 8.5

14. m∠ P < 54.88, m∠ N < 35.28, PN < 20.8

15. TU < 14.1, TS < 5.1, m∠ U 5 208

16. m∠ V 5 408, DM < 17.6, DV < 27.4

17. m∠ T < 61.98, m∠ A < 28.18, AT 5 34

18. UM < 9.9, m∠ U < 56.48, m∠ E < 33.68

19. m∠ A < 26.78 20. m∠ A < 42.08

21. m∠ A < 49.58 22. m∠ A < 71.38

23. m∠ A < 79.18 24. m∠ A < 76.18

25. m∠ A < 8.68 26. m∠ A < 48.78 27. B

28. 78.58 29. about 658 30. 111 ft

Practice Level B

1. 16.6 2. 65.08 3. 25.0 4. m∠P 5 538, PQ < 13.2, QR < 17.6 5. m∠P < 58.68, m∠N < 31.48, PN < 21.1 6. TU < 21.9, m∠S 5 72.38, m∠U 5 17.78 7. m∠V 5 398, DM < 11.3, DV < 18.0 8. m∠T 5 668, TR < 14.7, AT < 36.1 9. UM < 20.6, m∠U < 42.78, m∠E < 47.38 10. m∠C 5 648, AB < 4.0, BC < 2.0 11. m∠V 5 708, VW < 4.1, WX < 11.3 12. m∠J 5 58.48, JL < 13.4, LK < 11.4 13. 21.18 14. 38.78

15. 15.78 16. 69.58 17. 22.88 18. 83.78

19. 70.18 20. 39.68 21. about 84.02 ft

22. about 499.30 ft 23. about 191.5 in. or about 15 ft 11.5 in.; about 4.28; Yes, the angle is less than 4.788.

24. 71.8 in.

4.7886 in.72 in.

25. about 1039.2 ft 26. about 1648.5 ft

27. about 609.3 ft

Practice Level C

1. m∠ A 5 51.98 2. m∠ A 5 74.98

3. m∠ A 5 11.58

4. m∠ P 5 578, PQ < 9.8, QR < 15.1

5. m∠ P < 59.78, m∠ N < 30.38, PN < 13.9

6. JL < 10.2, LK < 4.7, m∠ J 5 27.78

7. m∠ V 5 738, WX < 32.5, WV < 9.9

8. m∠ C 5 64.58, AB < 3.7, BC < 1.8

9. UM < 17.2, m∠ U < 17.18, m∠ E < 72.98

10. TR < 2.2, RA < 6.1, m∠ T 5 708

Lesson 7.6, continuedA

NS

WE

RS

LAHGE11FLCRB_BMv2_C07_A01-A10.indd A9LAHGE11FLCRB_BMv2_C07_A01-A10.indd A9 10/16/09 10:04:49 AM10/16/09 10:04:49 AM

Copy

right

© H

olt M

cDou

gal.

All r

ight

s re

serv

ed.

A10GeometryChapter 7 Resource Book

11. MD < 20.6, VD < 23.2, m∠ V 5 62.88

12. UT < 30.4, m∠ U < 13.98, m∠ S < 76.18

13. m∠ A < 9.28 14. m∠ A < 60.98

15. m∠ A < 75.98 16. m∠ A < 75.58

17. m∠ A < 83.28 18. m∠ A < 35.98

19. m∠ A < 26.18 20. m∠ A < 87.18

21. m∠ A 5 458 22. m∠ A 5 908

23. m∠ A 5 908 24. m∠ A 5 08 25. 33 yd

26. 26.68 27. 463 ft 28. 186 ft 29. 400 ft

30. 258

Review for Mastery

1. 66.08 2. 31.08 3. 71.88 4. 13.38 5. 83.18

6. 47.98 7. angle measures: 298, 618, 908; side lengths: 21, 37.9, 43.3

8. angle measures: 238, 678, 908; side lengths: 6.4, 15, 16.3

Problem Solving Workshop:Mixed Problem Solving

1. a. about 15.68 b. about 2.3 mi

2. a.

you friend25 ft798

b. You can use the tangent ratio to fi nd the distance from your friend to the tree; 128.6 ft

c. about 41.4 ft

3. 39 in. 4. a. about 32.5 b. about 42.5

5. about 3.4 ft; The vertical distance between the crossbar and you is 10 2 5.5 5 4.5 feet and the angle of elevation is 538.

Use the tangent ratio tan 538 5 4.5

} x and solve for

x to fi nd the horizontal distance between you and the crossbar.

6. a. about 13.3 cm b. about 27.18; Answers will vary. c. Answers will vary.

Challenge Practice

1.

ah

B

A D C

c

b

sin C 5 h } a so, h 5 a sin C;

sin A 5 h } c so, h 5 c sin A.

a sin C 5 c sin A or sin C

} c 5

sin A } a .

a

g

B

A C

E

b

c

sin B 5 g } a so, g 5 a sin B

sin A 5 g }

b so, g 5 b sin A.

a sin B 5 b sin A or sin A

} a 5

sin B }

b .

sin A

} a 5

sin B }

b 5

sin C } c

2. c2 5 x2 1 y2; x 5 c cos Aa2 5 b2 1 2bx 1 x2 1 y2

a2 5 b2 1 c2 2 2bc cos A

3. a. c2 5 x2 1 y2; x 5 c cos Bb2 5 a2 2 2ax 1 x2 1 y2

b2 5 a2 1 c2 2 2ac cos Bb. a2 5 x2 1 y2; x 5 a cos Cc2 5 b2 2 2bx 1 x2 1 y2

c2 5 a2 1 b2 2 2ab cos C

4. (7.39, 3.06), (5.66, 5.66), (3.06, 7.39), (0, 8)

Chapter Review GameTriangle 1

2

7 6

5 3 6

Triangle 2

5

4 1

5 1 8

1. 6 2. 7 3. 2 4. 5 5. 6 6. 3 7. 1 8. 5

9. 1 10. 4 11. 8 12. 5

Lesson 7.7, continuedA

NS

WE

RS

LAHGE11FLCRB_BMv2_C07_A01-A10.indd A10LAHGE11FLCRB_BMv2_C07_A01-A10.indd A10 10/16/09 10:01:24 AM10/16/09 10:01:24 AM