P 12 Q - menihek.ca Pages/Teacher Pages/Paula Kelly_files/Math... · Determine the tangent ratio for K. L K M 12 37 a. 12 35 b. 12 37 c. 37 12 d. 35 12 8. ... 9.5 mm 10

Math 1201 Review Chapter 2

Multiple Choice

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

____ 1. Determine tan Q and tan R.

P

R

Q

16

12

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

____ 2. Determine the measure of N to the nearest tenth of a degree.

K

NM

7

13

a. 57.4° b. 61.7° c. 32.6° d. 28.3°

____ 3. 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°

____ 4. Determine the measure of ABD to the nearest tenth of a degree.

A B

C

8

19

D

| |

cm

cm

a. 65.1° b. 67.2° c. 22.8° d. 24.9°

____ 5. 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.

60 m

45 m

C

BA

D

a. 37° b. 41° c. 53° d. 49°

____ 6. 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°

____ 7. Determine the tangent ratio for K.

L

K

M

12

37

a. 12

35

b. 12

37

c. 37

12

d. 35

12

____ 8. Determine the length of side l to the nearest tenth of a metre.

L

N

M

66

12.2 m

°

l

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

____ 9. Determine the length of side s to the nearest tenth of a millimetre.

R

ST

25

20.3 mm

°

s

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

____ 10. 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

____ 11. 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

____ 12. Terry is lying on the ground near the B.C. Legislature Building. The angle between the ground and his line of

sight to the highest point on the building is 53 . The height of the building, from the ground to its highest point, is about 43 m. About how far is Terry from a point on the ground vertically below the highest point on

the building? Give the answer to the nearest metre.

a. 71 m b. 57 m c. 34 m d. 32 m

____ 13. A road has an angle of inclination of 16 . Determine the increase in altitude of the road, to the nearest metre, for every 150 m of horizontal distance.

a. 523 m b. 144 m c. 43 m d. 41 m

____ 14. 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

____ 15. Determine sin G and cos G to the nearest hundredth.

13

84

85

G

EF

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

____ 16. Determine the measure of Q to the nearest tenth of a degree.

P

R

Q

19

7

a. 68.4° b. 69.8° c. 21.6° d. 20.2°

____ 17. 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°

____ 18. Determine the measure of Y to the nearest tenth of a degree.

11.05.1

Y

WX

a. 27.6 b. 62.4 c. 65.1 d. 24.9

____ 19. 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

____ 20. A rope that supports a canopy is 8.5 m long. The rope is attached to the canopy at a point that is 7.5 m above

the ground. What is the angle of inclination of the rope to the nearest tenth of a degree?

a. 48.6 b. 61.9 c. 28.1 d. 41.4

____ 21. Determine the measure of B to the nearest tenth of a degree.

A

BC

D

25

17

a. 94.3 b. 34.2 c. 42.8 d. 47.2

____ 22. Determine the length of XY to the nearest tenth of a centimetre.

61°17.4 cm

XY

Z

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

____ 23. Determine the length of DE to the nearest tenth of a centimetre.

29°

7.7 cm

D

E F

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

____ 24. 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

____ 25. A surveyor made the measurements shown in the diagram. Determine the distance from R to S, to the nearest

hundredth of a metre.

Q

R

S

56.5°

38.91 m

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

____ 26. 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

____ 27. A balloon is flying at the end of a 170-m length of string, which is anchored to the ground. The angle of

inclination of the string is 50 . Calculate the height of the balloon to the nearest metre.

a. 130 m b. 143 m c. 109 m d. 222 m

____ 28. Determine the area of to the nearest square centimetre.

R

ST

21°

23.3 cm

a. 291 cm2 b. 707 cm

2 c. 104 cm

2 d. 208 cm

2

____ 29. 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?

55 yd.

34° 29°

treetree

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

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

Short Answer

30. A tree is supported by a guy wire. The guy wire is anchored to the ground 7.0 m from the base of the tree. The angle between the wire and the level ground is 60°. How far up the tree does the wire reach, to the nearest

tenth of a metre?

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

25°

||

24.0 cm

32. Solve this right triangle. Give the measures to the nearest tenth.

26°

9.1 cm

D

EF

33. Determine the length of WX to the nearest tenth of a centimetre.

W

Z

Y

X

9.5 cm 29°

31°

34. Calculate the measure of ABC to the nearest degree.

A

B

C

10 cm

9 cm 13 cm

35. 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.

62°

49°

80 ft.

36. Calculate the measure of ABC to the nearest tenth of a degree.

A

B

C

D

7 cm

4 cm

13 cm

37. Determine the length of RS to the nearest tenth of a centimetre.

54°8.9 cm

T

S

R

Q

39°

Problem

38. In the diagram below, a Coast Guard patrol boat is at C, which is 11.7 km south of Point Atkinson lighthouse.

A sailboat in distress is at A, which is 7.3 km west of the lighthouse.

a) How far is the patrol boat from the sailboat, to the nearest tenth of a kilometre?

b) At what angle to BC should the patrol boat travel to reach the sailboat? Give the answer to the nearest tenth of a degree.

A B

C

11.7

7.3

km

km

39. Determine the measures of and to the nearest tenth of a degree.

A B

C3

4

D

40. Three squares with side length 9 mm are placed side-by-side as shown. Thomas says ACB is approximately

71.6 .

a) Is he correct? Justify your answer. b) Describe what the value of tan C indicates.

A B

C

9

D

mm

E

G

41. A guy wire is connected from a tower to the ground. Determine the height of the tower, to the nearest tenth of

a metre. What assumptions about the ground are you making?

49

A

D

°

30.1 mE

42. The angle between one longer side of a rectangle and a diagonal is 37°. One shorter side of the rectangle is

6.2 cm.

a) Sketch and label the rectangle.

b) What is the length of the rectangle to the nearest tenth of a centimetre?

43. Determine the area of ABC to the nearest tenth of a square unit. Determine its perimeter to the nearest tenth of a unit.

A B

C

57°

23.6

44. A boat was docked 30.0 m from the base of a cliff. A sailor used a clinometer to sight the top of the cliff. The

angle between the horizontal and the line of sight was 74°. The sailor held the clinometer 1.5 m above the

surface of the water. Determine the height of the cliff to the nearest tenth of a metre.

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

22 ft.

12 ft. rafters

46. Determine the measures of A and C to the nearest tenth of a degree.

A B

C

11

23

47. Determine the area of this right triangle to the nearest square metre.

L

M N

850 m

57°

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

/\

9.0 cm

34°

A

BC

D

49. Solve XYZ. Give the measures to the nearest tenth. Explain your strategy. X Y

Z

18.9 cm

45°

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

22.1 cm129°

| |

Math 1201 Review Chapter 2

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: Easy REF: 2.1 The Tangent Ratio

LOC: 10.M4 TOP: Measurement KEY: Procedural Knowledge

2. ANS: D PTS: 1 DIF: Easy REF: 2.1 The Tangent Ratio


3. ANS: C PTS: 1 DIF: Moderate REF: 2.1 The Tangent Ratio LOC: 10.M4 TOP: Measurement KEY: Procedural Knowledge

4. ANS: B PTS: 1 DIF: Moderate REF: 2.1 The Tangent Ratio


5. ANS: A PTS: 1 DIF: Easy REF: 2.1 The Tangent Ratio


6. ANS: A PTS: 1 DIF: Moderate REF: 2.1 The Tangent Ratio


7. ANS: D PTS: 1 DIF: Moderate REF: 2.1 The Tangent Ratio


8. ANS: A PTS: 1 DIF: Easy REF: 2.2 Using the Tangent Ratio to Calculate Lengths LOC: 10.M4

TOP: Measurement KEY: Procedural Knowledge

9. ANS: D PTS: 1 DIF: Easy REF: 2.2 Using the Tangent Ratio to Calculate Lengths LOC: 10.M4


10. ANS: D PTS: 1 DIF: Moderate

REF: 2.2 Using the Tangent Ratio to Calculate Lengths LOC: 10.M4


11. ANS: C PTS: 1 DIF: Moderate



12. ANS: D PTS: 1 DIF: Moderate






14. ANS: C PTS: 1 DIF: Easy

REF: 2.3 Math Lab: Measuring an Inaccessible Height LOC: 10.M4 TOP: Measurement KEY: Procedural Knowledge

15. ANS: D PTS: 1 DIF: Easy REF: 2.4 The Sine and Cosine Ratios


16. ANS: A PTS: 1 DIF: Easy REF: 2.4 The Sine and Cosine Ratios


17. ANS: C PTS: 1 DIF: Moderate REF: 2.4 The Sine and Cosine Ratios


18. ANS: B PTS: 1 DIF: Easy REF: 2.4 The Sine and Cosine Ratios LOC: 10.M4 TOP: Measurement KEY: Procedural Knowledge

19. ANS: A PTS: 1 DIF: Moderate REF: 2.4 The Sine and Cosine Ratios


20. ANS: B PTS: 1 DIF: Moderate REF: 2.4 The Sine and Cosine Ratios


21. ANS: C PTS: 1 DIF: Easy REF: 2.4 The Sine and Cosine Ratios


22. ANS: B PTS: 1 DIF: Easy REF: 2.5 Using the Sine and Cosine Ratios to Calculate Lengths


23. ANS: B PTS: 1 DIF: Moderate

REF: 2.5 Using the Sine and Cosine Ratios to Calculate Lengths





25. ANS: B PTS: 1 DIF: Easy



26. ANS: C PTS: 1 DIF: Easy



27. ANS: A PTS: 1 DIF: Easy




REF: 2.6 Applying the Trigonometric Ratios LOC: 10.M4 TOP: Measurement KEY: Procedural Knowledge

29. ANS: B PTS: 1 DIF: Easy

REF: 2.7 Solving Problems Involving More than One Right Triangle LOC: 10.M4 TOP: Measurement KEY: Procedural Knowledge

SHORT ANSWER

30. ANS: 12.1 m

PTS: 1 DIF: Moderate REF: 2.2 Using the Tangent Ratio to Calculate Lengths


31. ANS:

23.4 cm

PTS: 1 DIF: Difficult REF: 2.5 Using the Sine and Cosine Ratios to Calculate Lengths


32. ANS:

EF = 18.7 cm

DF = 20.8 cm

D = 64.0

PTS: 1 DIF: Easy REF: 2.6 Applying the Trigonometric Ratios


33. ANS:

16.1 cm

PTS: 1 DIF: Moderate

REF: 2.7 Solving Problems Involving More than One Right Triangle


34. ANS:

94

PTS: 1 DIF: Easy



35. ANS:

129 ft.




36. ANS:


REF: 2.7 Solving Problems Involving More than One Right Triangle LOC: 10.M4 TOP: Measurement KEY: Procedural Knowledge

37. ANS:

cm

PTS: 1 DIF: Easy



PROBLEM

38. ANS:

a)

Use the Pythagorean Theorem in right ABC.

The Coast Guard patrol boat is approximately 13.8 km from the sailboat.

b)

Use the tangent ratio in right ABC.

The patrol boat should travel at an angle of approximately 32.0 to BC to reach the sailboat.

PTS: 1 DIF: Moderate REF: 2.1 The Tangent Ratio

LOC: 10.M4 TOP: Measurement KEY: Problem-Solving Skills

39. ANS:

Determine the measure of in right BDC.

Determine the measure of .



40. ANS:

a)

AB = mm

In right ABC:

Thomas is correct.

b)

In ABC above, tan C indicates that the length of the side opposite C is 3 times the length of the side

adjacent to C.


LOC: 10.M4 TOP: Measurement KEY: Communication | Problem-Solving Skills

41. ANS:

In right AED, side DE is opposite A and AE is adjacent to A.

Solve the equation for AE.

The height of the tower is approximately 26.2 m.

I am assuming the ground is horizontal.

PTS: 1 DIF: Moderate REF: 2.2 Using the Tangent Ratio to Calculate Lengths

LOC: 10.M4 TOP: Measurement

KEY: Communication | Problem-Solving Skills

42. ANS:

a)

A B

CD37

6.2 cm

°

b)

In right DCB, BC is opposite D and CD is adjacent to D.

Solve the equation for CD.

The length of the rectangle is approximately 8.2 cm.

PTS: 1 DIF: Moderate REF: 2.2 Using the Tangent Ratio to Calculate Lengths LOC: 10.M4 TOP: Measurement KEY: Problem-Solving Skills

43. ANS: Determine the length of AB.

In right ABC, AB is opposite C and BC is adjacent to C.

Solve the equation for AB.

Find the area of ABC.

The area of ABC is approximately 428.8 square units.

Determine the length of AC.

Use the Pythagorean Theorem in right ABC.

The perimeter of ABC is:

The perimeter of ABC is approximately 103.3 units.

PTS: 1 DIF: Difficult REF: 2.2 Using the Tangent Ratio to Calculate Lengths


44. ANS:

Sketch and label a diagram to represent the information in the problem.

In right ABC, BC is opposite A and AC is adjacent to A.

Solve this equation for BC.

74°

30.0 m1.5 m

A

B

C

D

Find the height, h, of the cliff.

The height of the cliff is approximately 106.1 m.

PTS: 1 DIF: Moderate REF: 2.3 Math Lab: Measuring an Inaccessible Height LOC: 10.M4 TOP: Measurement KEY: Problem-Solving Skills

45. ANS:

Draw a diagram to represent the cross-section of the roof.

Find BC.

In right ABC:

A

C B11 ft.

12 ft.

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

PTS: 1 DIF: Moderate REF: 2.4 The Sine and Cosine Ratios


46. ANS: Determine the measure of first.

In right ABC:

C is approximately 61.4° and A is approximately 28.6°.

PTS: 1 DIF: Moderate REF: 2.4 The Sine and Cosine Ratios


47. ANS:

In right LMN, LN is the hypotenuse, LM is opposite N, and MN is adjacent to N. Use the sine ratio to determine the height of the triangle, LM.

Solve this equation for LM.

Use the cosine ratio to determine the length of MN, the base of the triangle.

Solve this equation for MN.

Use the formula for the area, A, of a triangle.

The area of the triangle is approximately 165 009 m .

PTS: 1 DIF: Difficult



48. ANS:

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.

Solve this equation for AD.

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

Solve this equation for CD.

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

he perimeter of the triangle is approximately 58.9 cm.

PTS: 1 DIF: Difficult REF: 2.5 Using the Sine and Cosine Ratios to Calculate Lengths


49. ANS:

The acute angles in a right triangle have a sum of 90°.

In right XYZ:

Determine the length of XY.

Since XY is opposite Z and YZ is adjacent to Z, use the tangent ratio.

XY is approximately 18.9 cm.

Determine the length of XZ.

Since YZ is adjacent to Z and XZ is the hypotenuse, use the cosine ratio.

XZ is approximately 26.7 cm.

PTS: 1 DIF: Moderate REF: 2.6 Applying the Trigonometric Ratios

LOC: 10.M4 TOP: Measurement

KEY: Communication | Problem-Solving Skills

50. ANS:

Label a diagram.

ABD is an isosceles triangle, so each base

angle is:

Determine the height, AC, of the triangle.

In right ABC, AC is opposite B and AB is the hypotenuse.

22.1 cm129°

| |

25.5° 25.5°

A

BC

D

So, use the sine ratio in ABC.

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.

The base, BD, is:

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

The area of the triangle is approximately 189.8 cm

2.

PTS: 1 DIF: Difficult

REF: 2.7 Solving Problems Involving More than One Right Triangle LOC: 10.M4 TOP: Measurement KEY: Problem-Solving Skills

Documents

P 12 Q - menihek.ca Pages/Teacher Pages/Paula Kelly_files/Math... · Determine the tangent ratio for K. L K M 12 37 a. 12 35 b. 12 37 c. 37 12 d. 35 12 ____ 8. ... 9.5 mm ____ 10

P 12 Q - menihek.ca Pages/Teacher Pages/Paula Kelly_files/Math... · Determine the tangent ratio for K. L K M 12 37 a. 12 35 b. 12 37 c. 37 12 d. 35 12 8. ... 9.5 mm 10