9.1 Practice A · PDF file9.1 Practice A Name ... the statement of the tangent ratio for the...

Copyright © Big Ideas Learning, LLC Geometry All rights reserved. Resources by Chapter

291

9.1 Practice A

Name _________________________________________________________ Date __________

In Exercises 1–6, find the value of x. Then tell whether the side lengths form a Pythagorean triple.

1. 2. 3.

4. 5. 6.

In Exercises 7 and 8, tell whether the triangle is a right triangle.

7. 8.

In Exercises 9–12, verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse?

9. 5, 12, and 13 10. 5, 7, and 8

11. 2, 10, and 11 12. 8, 4, and 6

13. A ski lift forms a right triangle, as shown. Use the Pythagorean Theorem (Theorem 9.1) to approximate the horizontal distance traveled by a person riding the ski lift. Round your answer to the nearest whole foot.

34

x

7

7

x 2920

x

136

x

12 14

x

1630

x

57

3

75 5

11 2

1170 ft5750 ft

x

Geometry Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. 292

9.1 Practice B

Name _________________________________________________________ Date _________

In Exercises 1–3, find the value of x. Then tell whether the side lengths form a Pythagorean triple.

1. 2. 3.

In Exercises 4 and 5, tell whether the triangle is a right triangle.

4. 5.

6. You construct a picture frame with a diagonal piece attached to the back for support, as shown. Can you tell from the dimensions whether the corners of the frame are right angles? Explain.

In Exercises 7–9, verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse?

7. 14, 48, and 50 8. 7.1, 13.3, and 19.5 9. 67, 4, and 9

10. A triangle has side lengths of 12 feet and 18 feet. Your friend claims that the third side must be greater than 6 feet. Is your friend correct? Explain.

11. The diagram shows the design of a house roof. Each side of the roof is 24 feet long, as shown. Use the Pythagorean Theorem (Theorem 9.1) to answer each question.

a. What is the approximate width w of the house?

b. What is the approximate height h of the roof above the ceiling?

16

8

x

40 9

x

13

6x

1.63.1

3.4

2 3

719

39 in. 15 in.

36 in.

24 ft24 fth

w


9.2 Practice A

Name _________________________________________________________ Date _________

In Exercises 1–3, find the value of x. Write your answer in simplest form.

1. 2. 3.

In Exercises 4–6, find the values of x and y. Write your answers in simplest form.

4. 5. 6.

In Exercises 7 and 8, find the area of the figure. Round decimal answers to the nearest tenth.

7. 8.

9. A 12-foot ladder is leaning up against a wall, as shown. How high does the ladder reach up the wall when x is 30 ? 45 ? 60 ?° ° ° Round decimal answers to the nearest tenth, if necessary.

45°x

x

45°

4 2

45°

x

45°

345°

x45°

55

60°

xy 30°

1

60°

x

y30°

4 3

60°

x

y

30°10

11 m

20 yd


297

9.2 Practice B

Name _________________________________________________________ Date __________

In Exercises 1 and 2, copy and complete the table. Write your answers in simplest form.

1. 2.

3. The side lengths of a triangle are given. Determine whether each triangle is a - -45 45 90° ° ° triangle, a - -30 60 90° ° ° triangle, or neither.

a. 5, 10, 5 3 b. 7, 7, 7 3 c. 6, 6, 6 2

In Exercises 4–6, find the values of the variables. Write your answers in simplest form.

4. 5. 6.

7. You build a two-person tent, as shown. How many square feet of material is needed to make the tent, assuming the tent has a floor?

x 5 2

y 4 2 24

a 11

b 9 5 3

c 16

45°x

yx

45°

60°

bc

a

30°

60°

x

y

6

6

x

y

24

x

y

z

1630°

105°

60°6 ft

4 ft


301

9.3 Practice A

Name _________________________________________________________ Date __________

In Exercises 1 and 2, identify the similar triangles.

1. 2.

In Exercises 3–5, find the value of x.

3. 4. 5.

In Exercises 6–8, find the geometric mean of the two numbers.

6. 3 and 12 7. 4 and 14 8. 10 and 24


9. 10. 11.

12. You are designing a diamond-shaped kite. You know that 38.4 centimeters,AB = 72 centimeters, and 81.6 centimeters.BC AC= = You want to use a straight

crossbar .BD About how long should it be?

M LJ

K

Z

U

Y

X

Z W

x

Y

X

86

10

x20 21

29

x

8

1517

x32

24

x

126

x

18 8

A

B

C

D


9.3 Practice B

Name _________________________________________________________ Date _________

In Exercises 1–3, use the diagram.

1. Identify the similar triangles.

2. Which segment’s length is the geometric mean of AB and DB?

3. Find CD, AD, and AC.


4. 5. 6.

In Exercises 7–9, find the geometric mean of the two numbers.

7. 12 and 24 8. 16 and 25 9. 12 and 40

In Exercises 10–12, find the value(s) of the variable(s).

10. 11. 12.

13. You build a cornhole game. The game is constructed from a sheet of plywood supported by two boards. The two boards form a right angle and their lengths are 12 inches and 46.5 inches.

a. Find the length x of the plywood to the nearest inch.

b. You put in a support that is altitude y to the hypotenuse of the right triangle. What is the length of the support? Round your answer to the nearest tenth.

c. Where does the support attach to the plywood? Explain.

A

B

C

D

10

6

x 4030 x

5

35

x

10

6

w + 9

188y

z

x

11

9

y

zx

16

14

y

46.5 in.

12 in.

x in.


9.4 Practice A

Name _________________________________________________________ Date _________

1. Find the tangents of the acute angles in the right triangle. Write each answer as a fraction and as a decimal rounded to four decimal places.

2. Describe and correct the error in writing the statement of the tangent ratio for the given figure.

In Exercises 3–8, find the value of x. Round your answer to the nearest tenth.

3. 4. 5.

6. 7. 8.

9. You are measuring the height of a water slide. You stand 58 meters from the base of the slide. You measure the angle of elevation from the ground to the top of the water slide to be 13 .° Find the height h of the slide to the nearest meter.

R

TS

10

24

26

L

K

J

24

32

40

x

29

65°

x

370°

x 15

40°

x40

58°

x

9

45°

x

30°3

58 m13°

h


307

9.4 Practice B

Name _________________________________________________________ Date __________

In Exercises 1 and 2, find the tangents of the acute angles in the right triangle. Write each answer as a fraction and as a decimal rounded to four decimal places.

1. 2.

3. Draw and label the sides and angles of a triangle for which the tangents of the acute angles are equal to 1.

In Exercises 4–6, find the value(s) of the variable(s). Round your answer(s) to the nearest tenth.

4. 5. 6.

7. A surveyor is standing 30 feet from the base of a tall building. The surveyor measures the angle of elevation from the ground to the top of the building to be 65 .° Find the height h of the building to the nearest foot.

8. In the diagram, , 32 , 24 , and 14.RQ PQ m QPS m RPS PQ⊥ ∠ = ° ∠ = ° = Find RS to the nearest tenth of a unit.

50J

L

K48

14

D

EF

39

6 2

53

x

23°36 x

43°

82

x

y45° 28°

30 ft

h

65°

14

P

RQ S

24°32°


311

9.5 Practice A

Name _________________________________________________________ Date __________

In Exercises 1 and 2, find sin J, sin K, cos J, and cos K. Write each answer as a fraction and as a decimal rounded to four places.

1. 2.

In Exercises 3–6, write the expression in terms of sine or cosine.

3. sin 22° 4. cos 56° 5. cos 15° 6. sin 37°

In Exercises 7–9, find the value of each variable using sine and cosine. Round your answers to the nearest tenth.

7. 8. 9.

10. Which statement cannot be true? Explain.

A. sin 0.5A = B. sin 1.2654A =

C. sin 0.9962A = D. 34sin A =

11. The angle of depression is 11° from the bottom of a boat to a deep sea diver at a depth of 120 feet. Find the distance x the diver must swim up to the boat to the nearest foot.

J

KL

513

12 J

KL

16

30

34

a

b 2536°

x y

2543°

rs

11720°

A

B

CNot drawn to scale

120 ftx ft


9.5 Practice B

Name _________________________________________________________ Date _________

In Exercises 1 and 2, find sin R, sin S, cos R, and cos S. Write each answer as a fraction and as a decimal rounded to four places.

1. 2.

In Exercises 3–5, write the expression in terms of sine and/or cosine.

3. sin 7° 4. cos 31° 5. tan 60°

In Exercises 6–8, find the value of each variable using sine and cosine. Round your answers to the nearest tenth.

6. 7. 8.

9. Find the perimeter of the figure shown. Round your answer to the nearest centimeter.

10. You use an extension ladder to repair a chimney that is 33 feet tall. The length of the extension ladder ranges in one-foot increments from its minimum length to its maximum length. For safety reasons, you should always use an angle of about 75.5° between the ground and your ladder.

a. Your smallest extension ladder has maximum length of 17 feet. How high does this ladder safely reach on the chimney? Round your answer to the nearest tenth of a foot.

b. You place the ladder 3 feet from the base of the chimney. How many feet long should the ladder be? Round your answer to the nearest foot.

c. To reach the top of the chimney, you need a ladder that reaches 30 feet high. How many feet long should the ladder be? Round your answer to the nearest foot.

T S

R

1450

48T

SR 12

2 7

q

p20°

12

x

y39°

44

ab

57°

14

60°

55°55°

1.5 cm

75.5°

33 ft


9.6 Practice A

Name _________________________________________________________ Date _________

In Exercises 1–3, determine which of the two acute angles has the given trigonometric ratio.

1. The sine of the angle is 817.

2. The cosine of the angle is 1517.

3. The tangent of the angle is 158 .

In Exercises 4–6, let B∠ be an acute angle. Use a calculator to approximate the measure of B∠ to the nearest tenth of a degree.

4. sin 0.64B = 5. cos 0.12B = 6. tan 2.18B =

In Exercises 7–9, solve the right triangle. Round decimal answers to the nearest tenth.

7. 8. 9.

10. Use the diagram to find the distance across the suspension bridge. Round your answer to the nearest foot.

11. Use the diagram to find the acute angle formed by Washington Boulevard and Willow Way. Round your answer to the nearest tenth.

QR

P

22

37°

E

F

D

19

28 C

B

A 14

51°

52 ft

32° 32° 32° 32° 32° 32°

52 ft 52 ft

5.4 mi

2.8 mi

Washington Blvd.

Willow Way

Main

St.Q

RS

817

15


317

9.6 Practice B

Name _________________________________________________________ Date __________

In Exercises 1 and 2, determine which of the two acute angles has the given trigonometric ratio.

1. The cosine of the angle is 3.4

2. The tangent of the angle is 3 7 .7

In Exercises 3–5, let H∠ be an acute angle. Use a calculator to approximate the measure of H∠ to the nearest tenth of a degree.

3. sin 0.41H = 4. cos 0.05H = 5. tan 5.18H =

In Exercises 6–8, solve the right triangle. Round decimal answers to the nearest tenth.

6. 7. 8.

9. You are in a hot air balloon that is 600 feet above the ground. You can see two people. The angles of depression to person B and to person C are 30° and 20 ,° respectively.

a. How far is person B from the point on the ground below the hot air balloon?

b. How far is person C from the point on the ground below the hot air balloon?

c. How far apart are the two people?

10. On a typographic map, the contour lines show changes in elevation of the land. You and a friend are hiking on Kasatochi Island.

a. Find the difference in elevation (in miles) between you and your friend.

b. Use a ruler to find the horizontal distance (in miles) between you and your friend.

c. What is the angle of elevation from you to your friend?

T

S

R24°

33

D E

F

12

3 7

P

Q

R

7

23

600 ft

B C

20° 30°

Contour Interval 200 feet

0 0.5 miyou

your friend

200

400600

800

lake

Kasatochi Island

X

YW

8

6

2 7


321

9.7 Practice A

Name _________________________________________________________ Date __________

In Exercises 1–3, use a calculator to find the trigonometric ratio. Round your answer to four decimal places.

1. cos 115° 2. tan 95° 3. sin 148°

In Exercises 4 and 5, find the area of the triangle. Round your answer to the nearest tenth.

4. 5.

6. Place each triangle case into one of the three categories according to the first step in solving the triangle.

In Exercises 7–12, solve the triangle. Round decimal answers to the nearest tenth.

7. 8. 9.

10. 11. 12.

13. Determine the measure of angle A in the design of the streetlamp shown in the diagram.

Law of Sines Law of Cosines Neither

AAA AAS ASA SSS SSA SAS

C

B

A 1040°35°

C

BA

1216

18

CB

A

131°8

11

C

B

A

80°61

100

C

B

A7

4

9C

B

A

15

70°

36°

2 ft

3 ft

4 ft12

C

B

A 12 m

9 m

25°

C

BA

37 ft11 ft 135°


9.7 Practice B

Name _________________________________________________________ Date _________

In Exercises 1–3, use a calculator to find the trigonometric ratio. Round your answer to four decimal places.

1. tan 133° 2. cos 128° 3. sin 91°

In Exercises 4 and 5, find the area of the triangle. Round your answer to the nearest tenth.

4. 5.

6. A parking lot has the shape of a parallelogram, as shown. Explain how you can find the area of the parking lot without using right triangles. Then find the area of the parking lot.

In Exercises 7–12, solve the triangle. Round decimal answers to the nearest tenth.

7. 8. 9.

10. 11. 12.

13. A bike frame has a top tube length of 20.75 inches, a seat tube length of 8.9 inches, and a seat tube angle of 71 .°

a. Find the approximate length of the down tube.

b. Find the angle between the seat tube and down tube.

C

B

A112°

10.1 cm

12.9 cm

C

B

A

32°

6 in.

8 in.

100 m

70 m

70°

C

B

A

88°

59° 13

C

BA 1367°

5.8

C

B

A 3.678°

3.9

C

BA

6

10

7

C

B

A

12

85°

24°

C

B

A 15

10 8

20.75 in.

8.9 in.71°

top tube

down tube

seat tube

9.1 Practice A · PDF file9.1 Practice A Name ... the statement of the tangent ratio for the...

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