Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Math 10 - Unit 2 Final Review Worksheet - Trigonometry

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Determine sin G and cos G to the nearest hundredth.

a. sin G = 0.99; cos G = 6.54 c. sin G = 1.01; cos G = 0.15

b. sin G = 0.15; cos G = 0.99 d. sin G = 0.99; cos G = 0.15

____ 2. Determine tan A and tan C.

a. tan A = 1.25; tan C = 0.8 c. tan A = 0.8; tan C = 1.25

b. tan A = 0.8; tan C = 0.7809... d. tan A = 0.6247...; tan C = 1.25

____ 3. Determine the tangent ratio for ∠T.

a.12

35b.

37

35c.

35

37d.

35

12

Name: ________________________ ID: A

2

____ 4. Determine tan Q and tan R.

a. tan Q = 0.428571; tan R = 0.75 c. tan Q = 1.3; tan R = 0.571428

b. tan Q = 1.3; tan R = 0.75 d. tan Q = 0.75; tan R = 1.3

____ 5. Determine sin A and cos A to the nearest tenth.

a. sin A = 1.7; cos A = 0.8 c. sin A = 0.6; cos A = 1.3

b. sin A = 0.8; cos A = 0.6 d. sin A = 0.6; cos A = 0.8

____ 6. Determine the tangent ratio for ∠K.

a.12

35b.

12

37c.

37

12d.

35

12

Name: ________________________ ID: A

3

____ 7. Determine the measure of ∠N to the nearest tenth of a degree.

a. 57.4° b. 61.7° c. 32.6° d. 28.3°

____ 8. Determine the measure of ∠D to the nearest tenth of a degree.

a. 18.4° b. 19.5° c. 70.5° d. 71.6°

____ 9. Determine the measure of ∠Y to the nearest tenth of a degree.

a. 27.6° b. 62.4° c. 65.1° d. 24.9°

Name: ________________________ ID: A

4

____ 10. Determine the measure of ∠Q to the nearest tenth of a degree.

a. 68.4° b. 69.8° c. 21.6° d. 20.2°

____ 11. Determine the measure of ∠D to the nearest tenth of a degree.

a. 67.6° b. 69.1° c. 22.4° d. 20.9°

____ 12. Determine the measure of ∠ABD to the nearest tenth of a degree.

a. 65.1° b. 67.2° c. 22.8° d. 24.9°

____ 13. Determine the measure of ∠V to the nearest tenth of a degree.

a. 59.5° b. 36.1° c. 30.5° d. 53.9°

Name: ________________________ ID: A

5

____ 14. Determine the measure of ∠B to the nearest tenth of a degree.

a. 94.3° b. 34.2° c. 42.8° d. 47.2°

____ 15. Determine the length of RS to the nearest tenth of a metre.

a. 19.7 m b. 5.7 m c. 18.0 m d. 64.3 m

____ 16. Determine the length of side d to the nearest tenth of a centimetre.

a. 29.5 cm b. 27.7 cm c. 10.7 cm d. 3.7 cm

____ 17. Determine the length of DE to the nearest tenth of a centimetre.

a. 8.8 cm b. 15.9 cm c. 3.7 cm d. 13.9 cm

Name: ________________________ ID: A

6

____ 18. Determine the length of side z to the nearest tenth of a centimetre.

a. 9.7 cm b. 2.6 cm c. 5.4 cm d. 8.5 cm

____ 19. Determine the length of MN to the nearest tenth of an centimetre.

a. 36.9 cm b. 41.4 cm c. 8.5 cm d. 16.8 cm

____ 20. Determine the length of side l to the nearest tenth of a metre.

a. 5.4 m b. 27.4 m c. 11.1 m d. 5.0 m

____ 21. Determine the length of XY to the nearest tenth of a centimetre.

a. 8.4 cm b. 15.2 cm c. 31.4 cm d. 19.9 cm

Name: ________________________ ID: A

7

____ 22. Determine the length of side s to the nearest tenth of a millimetre.

a. 18.4 mm b. 43.5 mm c. 8.6 mm d. 9.5 mm

____ 23. Calculate the length of this rectangle to the nearest tenth of a metre.

a. 7.9 m b. 2.9 m c. 6.7 m d. 3.1 m

____ 24. Determine the angle of inclination of the line to the nearest tenth of a degree.

a. 63.3° b. 24.2° c. 65.8° d. 26.7°

____ 25. Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 22%.

a. 77.3° b. 77.6° c. 12.4° d. 12.7°

____ 26. A guy wire is attached to a tower at a point that is 10 m above the ground. The wire is anchored 21 m from

the base of the tower. What angle, to the nearest degree, does the guy wire make with the ground?

a. 62° b. 25° c. 28° d. 65°

____ 27. A guy wire is attached to a tower at a point that is 5.5 m above the ground. The angle between the wire and

the level ground is 56°. How far from the base of the tower is the wire anchored to the ground, to the nearest

tenth of a metre?

a. 3.1 m b. 6.6 m c. 3.7 m d. 8.2 m

Name: ________________________ ID: A

8

____ 28. A 55-ft. guy wire helps to support a tower. The wire is anchored to the ground 37 ft. from the base of the

tower. What is the measure of the angle formed between the wire and the ground, to the nearest degree?

a. 48° b. 56° c. 34° d. 42°

____ 29. From the start of a runway, the angle of elevation of an approaching airplane is 17.5°. At this time, the plane

is flying at an altitude of 7.7 km. How far is the plane from the start of the runway to the nearest tenth of a

kilometre?

a. 8.1 km b. 2.3 km c. 25.6 km d. 24.4 km

____ 30. A ladder leans against the side of a building. The top of the ladder is 5 m from the ground. The base of the

ladder is 1.0 m from the wall. What angle, to the nearest degree, does the ladder make with the ground?

a. 79° b. 11° c. 9° d. 83°

____ 31. A helicopter is hovering 200 m above a road. A car stopped on the side of the road is 300 m from the

helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree?

a. 56° b. 48° c. 42° d. 34°

____ 32. A student stood 8.0 m from the base of a tree. She used a clinometer to sight the top of the tree. The angle

shown on the protractor scale was 65°. The student held the clinometer 1.6 m above the ground. Determine

the height of the tree to the nearest tenth of a metre.

a. 10.4 m b. 5.3 m c. 3.7 m d. 18.8 m

____ 33. This cabin’s roof is built within 1° of the recommended angle for solar panels. Determine the approximate

latitude of the cabin, to the nearest degree.

a. 50° b. 34° c. 40° d. 56°

____ 34. From a point 18 ft. from the base of a flagpole, Seema used a clinometer to sight the top of the flagpole.

Seema held the clinometer 5 ft. 3 in. above the ground. The angle between the horizontal and the line of sight

was 52°. Determine the height of the flagpole to the nearest foot.

a. 28 ft. b. 34 ft. c. 19 ft. d. 23 ft.

Name: ________________________ ID: A

9

____ 35. A guy wire is attached to a tower at a point that is 7.5 m above the ground. The angle of inclination of the

wire is 67°. Determine the length of the wire to the nearest tenth of a metre.

a. 18.7 m b. 20.2 m c. 8.1 m d. 7.9 m

____ 36. A ladder is 13.0 m long. It leans against a wall. The base of the ladder is 3.7 m from the wall. What is the

angle of inclination of the ladder to the nearest tenth of a degree?

a. 73.5° b. 16.5° c. 74.1° d. 15.9°

____ 37. A ladder is 8.0 m long. It leans against a wall. The angle of inclination of the ladder is 72°. To the nearest

tenth of a metre, how far from the wall is the base of the ladder?

a. 2.6 m b. 7.6 m c. 25.9 m d. 2.5 m

____ 38. Rhonda walked diagonally across a rectangular playground with dimensions 60 m by 45 m. She started at

point C. Determine the angle, to the nearest degree, between her path and the longest side of the playground.

a. 37° b. 41° c. 53° d. 49°

____ 39. A surveyor held a clinometer 1.5 m above the ground from a point 60.0 m from the base of a tower. The

angle between the horizontal and the line of sight to the top of the tower was 21°. Determine the height of the

tower to the nearest tenth of a metre.

a. 157.8 m b. 23.0 m c. 24.5 m d. 65.8 m

____ 40. A wheelchair ramp is 7.0 m long. Its angle of inclination is 9°. Calculate the rise of the ramp to the nearest

tenth of a metre.

a. 1.0 m b. 44.7 m c. 1.1 m d. 6.9 m

Name: ________________________ ID: A

10

____ 41. A surveyor made the measurements shown in the diagram. Determine the distance from R to S, to the nearest

hundredth of a metre.

a. 46.66 m b. 70.50 m c. 25.75 m d. 58.79 m

____ 42. A ladder leans against a wall. The base of the ladder is on level ground 1.2 m from the wall. The angle

between the ladder and the ground is 70°. How far up the wall does the ladder reach, to the nearest tenth of a

metre?

a. 0.4 m b. 1.3 m c. 3.5 m d. 3.3 m

____ 43. Determine the measure of ∠DBC to the nearest tenth of a degree.

a. 27.5° b. 24.8° c. 65.2° d. 62.5°

____ 44. A helicopter is ascending vertically. On the ground, a searchlight is 125 m from the point where the

helicopter lifted off the ground. It shines on the helicopter and the angle the beam makes with the ground is

48°. How high is the helicopter at this point, to the nearest metre?

a. 187 m b. 93 m c. 113 m d. 139 m

Name: ________________________ ID: A

11

____ 45. Solve this right triangle. Give the measures to the nearest tenth.

a. ∠U = 26.6°; ∠W = 63.4°; UW = 14.5 cm c. ∠U = 63.4°; ∠W = 26.6°; UW = 29.1 cm

b. ∠U = 63.4°; ∠W = 26.6°; UW = 14.5 cm d. ∠U = 26.6°; ∠W = 63.4°; UW = 29.1 cm

____ 46. Solve this right triangle. Give the measures to the nearest tenth.

a. ∠J = 68.6°; ∠L = 21.4°; JL = 24.7 cm c. ∠J = 21.4°; ∠L = 68.6°; JL = 24.7 cm

b. ∠J = 68.6°; ∠L = 21.4°; JL = 63.1 cm d. ∠J = 21.4°; ∠L = 68.6°; JL = 63.1 cm

____ 47. Solve this right triangle. Give the measures to the nearest tenth.

a. ∠F = 67°; GH = 3.4 m; FH = 8.7 m c. ∠F = 77°; GH = 18.8 m; FH = 20.5 m

b. ∠F = 67°; GH = 18.8 m; FH = 8.7 m d. ∠F = 67°; GH = 18.8 m; FH = 20.5 m

Name: ________________________ ID: A

12

____ 48. Solve this right triangle. Give the measures to the nearest tenth.

a. ∠G = 40°; GH = 21.8 cm; FH = 18.3 cm c. ∠G = 40°; GH = 18.3 cm; FH = 21.8 cm

b. ∠G = 40°; GH = 21.8 cm; FH = 44.3 cm d. ∠G = 50°; GH = 21.8 cm; FH = 18.3 cm

____ 49. An architect draws this diagram of a wheelchair entrance ramp for a building. Determine the angle of

inclination of the ramp to the nearest tenth of a degree.

a. 86.7° b. 29.7° c. 3.3° d. 5.1°

____ 50. At a point 25 ft. from the base of a totem pole, the angle of elevation of the top of the pole is 50.1°. How tall

is the totem pole to the nearest foot?

a. 39 ft. b. 16 ft. c. 30 ft. d. 21 ft.

____ 51. A water taxi leaves its dock, and travels 7 km due north to pick up medical supplies. It then travels 15 km due

east to drop off the supplies at a hospital. To the nearest degree, what is the measure of the angle between the

path it took due east and the path it will take to return directly to its dock?

a. 25° b. 62° c. 28° d. 65°

____ 52. A road rises 1 m for every 19 m measured along the road. To the nearest metre, how far does a car travel

horizontally when it travels 300 m along the road?

a. 300 m b. 16 m c. 19 m d. 300 m

Name: ________________________ ID: A

13

____ 53. The front of a tent has the shape of an isosceles triangle with equal sides 163 cm long. The measure of the

angle at the peak of the tent is 105°. Calculate the maximum headroom in the tent to the nearest centimetre.

a. 129 cm b. 125 cm c. 99 cm d. 231 cm

____ 54. Determine the area of RST to the nearest square centimetre.

a. 291 cm2 b. 707 cm2 c. 104 cm2 d. 208 cm2

____ 55. Determine the perimeter of an equilateral triangle with height 11.9 cm. Give the measure to the nearest tenth

of a centimetre.

a. 81.8 cm b. 41.2 cm c. 30.9 cm d. 71.4 cm

____ 56. Determine the area of this rectangle to the nearest tenth of a square metre.

a. 54.0 m2 b. 420.2 m2 c. 98.1 m2 d. 61.9 m2

Name: ________________________ ID: A

14

____ 57. Determine the length of RS to the nearest tenth of a centimetre.

a. 6.7 cm b. 9.3 cm c. 11.4 cm d. 8.3 cm

____ 58. Determine the length of MN to the nearest tenth of a centimetre.

a. 5.2 cm b. 3.4 cm c. 2.9 cm d. 4.5 cm

____ 59. Two trees are 55 yd. apart. From a point halfway between the trees, the angles of elevation of the tops of the

trees are measured. What is the height of each tree to the nearest yard?

a. 33 yd.; 31 yd. c. 41 yd.; 50 yd.

b. 19 yd.; 15 yd. d. 40 yd.; 49 yd.

Name: ________________________ ID: A

15

____ 60. Determine the length of QR to the nearest metre.

a. 85 m b. 170 m c. 127 m d. 118 m

____ 61. Calculate the measure of ∠GHJ to the nearest tenth of a degree.

a. 77.5° b. 29.3° c. 60.7° d. 68.0°

____ 62. From the top of an 80-ft. building, the angle of elevation of the top of a taller building is 49° and the angle of

depression of the base of this building is 62°. Determine the height of the taller building to the nearest foot.

a. 211 ft. b. 112 ft. c. 129 ft. d. 276 ft.

Name: ________________________ ID: A

16

____ 63. Calculate the measure of ∠ABC to the nearest tenth of a degree.

a. 47.7° b. 102.5° c. 77.5° d. 52.6°

____ 64. Determine the length of AC to the nearest tenth of a centimetre.

a. 70.4 cm b. 141.6 cm c. 39.9 cm d. 41.9 cm

Short Answer

65. Determine the height of this isosceles triangle to the nearest tenth of a centimetre.

66. Tan B = 1.3; determine the measure of ∠B to the nearest tenth of a degree.

67. A road increases 8 m in altitude for every 100 m of horizontal distance. Calculate the angle of inclination of

the road, to the nearest tenth of a degree.

Name: ________________________ ID: A

17

68. Determine the angle of inclination of the line to the nearest tenth of a degree.

69. On a clinometer, how does the acute angle between the thread and the straw relate to the angle of inclination

of the straw?

Problem

70. Determine the perimeter of this triangle to the nearest tenth of a centimetre.

71. Guy wires are attached to buildings as shown. A student says the angles of inclination of the wires are the

same. Is the student correct? Justify your answer.

Name: ________________________ ID: A

18

72. Calculate the angle of inclination of the roof to the nearest tenth of a degree.

73. A Girl Guide measured the angle of elevation of the top of a monument as 59°. The height of the monument

is 38.5 m. She then walked 31.0 m due west from the point where she measured the angle of elevation.

Determine the angle of elevation of the monument from her new location to the nearest tenth of a degree.

74. Determine the area of this triangle to the nearest tenth of a square centimetre.

75. The length of the body diagonal in this rectangular prism is 61 cm. The width of the prism is 29 cm. The

measure of ∠AFH is 23°. Determine the height and the length of the rectangular prism to the nearest

centimetre.

ID: A

1

Math 10 - Unit 2 Final Review Worksheet - Trigonometry

Answer Section

MULTIPLE CHOICE

1. D

2. C

3. D

4. B

5. D

6. D

7. D

8. A

9. B

10. A

11. C

12. B

13. D

14. C

15. A

16. B

17. B

18. D

19. C

20. A

21. B

22. D

23. C

24. B

25. C

26. B

27. C

28. A

29. C

30. A

31. C

32. B

33. A

34. A

35. C

36. A

37. D

38. A

39. C

ID: A

2

40. C

41. B

42. D

43. B

44. D

45. B

46. C

47. D

48. A

49. C

50. C

51. A

52. D

53. C

54. C

55. B

56. A

57. D

58. A

59. B

60. D

61. C

62. C

63. D

64. D

SHORT ANSWER

65. 23.4 cm

66. ∠B =Ö 52.4°

67. 4.6°

68. 55.1°

69. The angle of inclination of the straw is equal to 90° minus the angle between the thread and the straw.

ID: A

3

PROBLEM

70. In right ∆ACD, AD is the hypotenuse, AC is opposite ∠D, and CD is adjacent to ∠D. To determine the

length of AD, use the sine ratio.

sinD =opposite

hypotenuse

sinD =AC

AD

sin34° =9.0

AD

Solve this equation for AD.

AD sin34° =(9.0)(AD)

AD

AD sin34° = 9.0

AD sin34°

sin34°=

9.0

sin34°

AD =9.0

sin34°

AD = 16.0946. . .

To determine the length of CD, use the cosine ratio.

cos D =adjacent

hypotenuse

cos D =CD

AD

cos 34° =CD

16.0946. . .

Solve this equation for CD.

(16.0946. . . ) cos 34° =(16.0946. . . )(CD)

16.0946. . .

(16.0946. . . ) cos 34° = CD

CD = 13.3430. . .

Since AD = AB and CD = BC, the perimeter, P, of the triangle is:

ID: A

4

P = AD + AB + CD + BC

P = 16.0946… + 16.0946… + 13.3430… + 13.3430…

P = 58.8753…

Τhe perimeter of the triangle is approximately 58.9 cm.

71.

∠C in right ∆ABC is the angle of inclination

of the guy wire attached to the shorter

building.

In right ∆ABC:

sinC =opposite

hypotenuse

sinC =AB

AC

sinC =35

47

∠C = 48.1316. . . °

The angle of inclination of the guy wire attached to the shorter building is approximately 48.1°.

∠F in right ∆DEF is the angle of inclination of the guy wire attached to the taller building.

In right ∆DEF:

cos F =adjacent

hypotenuse

cos F =EF

DF

cos F =37

52

∠F = 44.6397. . . °

The angle of inclination of the guy wire attached to the taller building is approximately 44.6°.

The student is not correct. The angles of inclination are different.

ID: A

5

72.

Draw a diagram to represent the cross-section

of the roof.

Find BC.

BC =22 ft.

2

BC = 11 ft.

In right ∆ABC:

cos C =adjacent

hypotenuse

cos C =BC

AC

cos C =11

12

∠C = 23.5564. . . °

The angle of inclination of the roof is approximately 23.6°.

ID: A

6

73. Label a diagram.

Use right ∆ACD to calculate the length of

CD. AD is opposite ∠ACD and CD is

adjacent to ∠ACD.

So, use the tangent ratio.

tanC =opposite

adjacent

tanC =AD

CD

tan59° =38.5

CD

CD tan59° = 38.5

CD =38.5

tan59°

CD = 23.1331…

Use right ∆ABD to calculate the measure of ∠B.

First determine the length of BD.

BD = BC + CD

BD = 31.0 + 23.1331…

BD = 54.1331…

Determine the measure of ∠B.

AD is opposite ∠B and BD is adjacent to ∠B.

So, use the tangent ratio.

tanB =opposite

adjacent

tanB =AD

BD

tanB =38.5

54.1331…

∠B = 35.4207…°

Τhe angle of elevation of the monument from the new location is approximately 35.4°.

ID: A

7

74. Label a diagram.

∆ABD is an isosceles triangle, so each base

angle is:

=180° − 129°

2

= 25.5°

Determine the height, AC, of the triangle.

In right ∆ABC, AC is opposite ∠B and AB is

the hypotenuse.

So, use the sine ratio in ∆ABC.

sinB =opposite

hypotenuse

sinB =AC

AB

sin25.5° =AC

22.1

22.1sin25.5° = AC

AC = 9.5142…

Determine the length of the base, BD, of ∆ABD

BD = 2(BC)

In right ∆ABC, BC is adjacent to ∠B and AB is the hypotenuse.

So, use the cosine ratio in ∆ACB.

cos B =adjacent

hypotenuse

cos B =BC

AB

cos 25.5° =BC

22.1

22.1cos 25.5° = BC

BC = 19.9471…

The base, BD, is:

BD = 2(BC)

BD = 2(19.9471…)

BD = 39.8942…

The formula for Area, A, of a triangle is:

ID: A

8

A =1

2bh

A =1

2(39.8942…)(9.5142…)

A = 189.7829…

The area of the triangle is approximately 189.8 cm2.

ID: A

9

75.

Determine the height of the prism.

In right ∆!AHF, the height, AH, is opposite

∠AFH and AF is the hypotenuse.

Use the sine ratio in ∆AHF.

sinF =opposite

hypotenuse

sinF =AH

AF

sin23° =AH

61

61sin23° = AH

AH = 23.8345…

The height of the prism is approximately 24 cm.

Determine the length of the prism.

In right ∆AHF, FH is adjacent to ∠AFH and AF is the hypotenuse.

Use the cosine ratio in ∆AHF.

cos F =adjacent

hypotenuse

cos F =FH

AF

cos 23° =FH

61

61cos 23° = FH

FH = 56.1507. . .

Use the Pythagorean Theorem in ∆EHF to determine the length of the prism, EF.

FH2

= EH2

+ EF2

56.1507…2

= 292

+ EF2

56.1507…2

− 292

= EF2

EF = 56.1507…2

− 292

EF = 48.0823…

Τhe length of the prism is approximately 48 cm.