# Quiz 7: Additional Topics in Trigonometry

Mathematics

Q 1Q 1

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

B

Q 2Q 2

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.
A)
B)
C)
D)
E) not possible

Free

Multiple Choice

D

Q 3Q 3

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 22.20 sq. units
B) 24.67 sq. units
C) 19.73 sq. units
D) 29.60 sq. units
E) 27.13 sq. units

Free

Multiple Choice

B

Q 4Q 4

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 33.24 sq. units
B) 29.91 sq. units
C) 39.89 sq. units
D) 26.59 sq. units
E) 36.56 sq. units

Free

Multiple Choice

Q 5Q 5

A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
A) 10.20 feet
B) 3.30 feet
C) 6.27 feet
D) 6.63 feet
E) 12.32 feet

Free

Multiple Choice

Q 6Q 6

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 7Q 7

Given , , and , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 8Q 8

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 9Q 9

Given , , and , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 10Q 10

Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.
A) 14.32
B) 15.33
C) 13.31
D) 21.37
E) 17.34

Free

Multiple Choice

Q 11Q 11

Given , , and , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
A) 17.88
B) 18.18
C) 15.73
D) 17.57
E) 16.96

Free

Multiple Choice

Q 12Q 12

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 13Q 13

In the figure below, , , and . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A) 9.12
B)
C) 5.87
D) 10.20
E) 11.64

Free

Multiple Choice

Q 14Q 14

In the figure below, , , and . Use this information to solve the parallelogram for . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 15Q 15

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A) 6.33
B) 5.91
C) 9.27
D) 7.59
E) 2.54

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 18Q 18

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]
A)
B)
C)
D) none of these
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 21Q 21

Find the vector v that has a magnitude of and is in the same direction as u, where .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 22Q 22

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Q 24Q 24

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 76.18 sq. units
B) 114.27 sq. units
C) 95.23 sq. units
D) 104.75 sq. units
E) 85.70 sq. units

Free

Multiple Choice

Q 25Q 25

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 26Q 26

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 27Q 27

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.
A)
B) not possible
C)
D)
E)

Free

Multiple Choice

Q 28Q 28

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 43.69 sq. units
B) 49.15 sq. units
C) 54.61 sq. units
D) 65.53 sq. units
E) 60.07 sq. units

Free

Multiple Choice

Q 29Q 29

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 34.18 sq. units
B) 37.29 sq. units
C) 27.97 sq. units
D) 31.07 sq. units
E) 24.86 sq. units

Free

Multiple Choice

Q 30Q 30

A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 6 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
A) 4.28 feet
B) 1.97 feet
C) 5.26 feet
D) 9.60 feet
E) 8.41 feet

Free

Multiple Choice

Q 31Q 31

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 32Q 32

Given , , and , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 33Q 33

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 34Q 34Given , , and , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 35Q 35

Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.
A) 9.25
B) 13.55
C) 17.84
D) 10.33
E) 11.40

Free

Multiple Choice

Q 36Q 36

Given , , and , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
A) 13.27
B) 9.13
C) 14.65
D) 13.96
E) 11.89

Free

Multiple Choice

Q 37Q 37Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 38Q 38

In the figure below, , , and . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A) 10.00
B) 7.21
C) 10.93
D)
E) 12.17

Free

Multiple Choice

Q 39Q 39

In the figure below, , , and . Use this information to solve the parallelogram for . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 40Q 40

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A) 15.33
B) 11.55
C) 13.44
D) 7.77
E) 12.02

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 43Q 43

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]
A)
B)
C)
D) none of these
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 46Q 46

Find the vector v that has a magnitude of and is in the same direction as u, where .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 47Q 47

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Q 49Q 49

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 30.00 sq. units
B) 27.00 sq. units
C) 33.00 sq. units
D) 36.00 sq. units
E) 24.00 sq. units

Free

Multiple Choice

Q 50Q 50Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 51Q 51Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 52Q 52

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.
A)
B)
C)
D)
E) not possible

Free

Multiple Choice

Q 53Q 53

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 43.69 sq. units
B) 36.41 sq. units
C) 29.12 sq. units
D) 32.77 sq. units
E) 40.05 sq. units

Free

Multiple Choice

Q 54Q 54

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 68.17 sq. units
B) 61.36 sq. units
C) 54.54 sq. units
D) 81.81 sq. units
E) 74.99 sq. units

Free

Multiple Choice

Q 55Q 55

A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 6 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
A) 3.49 feet
B) 6.31 feet
C) 5.71 feet
D) 8.26 feet
E) 4.15 feet

Free

Multiple Choice

Q 56Q 56Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 57Q 57Given , , and , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 58Q 58

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 59Q 59Given , , and , use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 60Q 60

Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.
A) 12.33
B) 17.78
C) 13.69
D) 23.24
E) 15.06

Free

Multiple Choice

Q 61Q 61

Given , , and , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
A) 19.48
B) 16.84
C) 20.36
D) 13.33
E) 18.60

Free

Multiple Choice

Q 62Q 62Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 63Q 63

In the figure below, , , and . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A)
B) 13.71
C) 12.25
D) 7.88
E) 11.16

Free

Multiple Choice

Q 64Q 64

In the figure below, , , and . Use this information to solve the parallelogram for . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 65Q 65

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.
A) 6.79
B) 12.92
C) 14.97
D) 11.39
E) 10.88

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 68Q 68

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]
A)
B)
C)
D) none of these
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 71Q 71

Find the vector v that has a magnitude of and is in the same direction as u, where .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 72Q 72

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Q 74Q 74

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 28.61 sq. units
B) 21.46 sq. units
C) 19.07 sq. units
D) 23.84 sq. units
E) 26.22 sq. units

Free

Multiple Choice

Q 75Q 75Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 76Q 76

Given that Force 1 = 70 pounds and Force 2 = 90 pounds, find the angle between the forces if the magnitude of the resultant force is 140 pounds. Round answer to the nearest degree.
A) 134°
B) 119°
C) 127°
D) 122°
E) 114°

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 80Q 80

Determine where is the angle between u and v. Round answer to two decimal places.
A) 7.07
B) 5.00
C) 6.83
D) 8.66
E) 6.04

Free

Multiple Choice

Q 81Q 81

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 6%.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 89Q 89

Find the standard form of the complex number shown below. Round answers to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 90Q 90

Find the standard form of the complex number . Round values to the nearest hundredth.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 91Q 91

Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 92Q 92

Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Q 94Q 94

Find the product using trigonometric forms. Leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 95Q 95

Use DeMoivre's Theorem to find the indicated power of the following complex number.
A) 16,384
B) 1,048,576
C) 32,768
D) -16,384
E) 262,144

Free

Multiple Choice

Q 96Q 96

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 97Q 97

Use DeMoivre's Theorem to find the indicated power of the following complex number.
A)
B) 32
C) 64
D) -64
E)

Free

Multiple Choice

Free

Multiple Choice

Q 99Q 99

Find the cube roots of the following complex number. Write each of the roots in standard form.
A) , ,
B) ,
C) , ,
D)
E) , ,

Free

Multiple Choice

Free

Multiple Choice

Q 101Q 101

Given that Force 1 = 70 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 90 pounds. Round answer to the nearest degree.
A) 60°
B) 40°
C) 53°
D) 45°
E) 48°

Free

Multiple Choice

Q 102Q 102

Given vectors and determine the quantity indicated below.
A) 12
B) -112
C) -44
D) -48
E) -144

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 105Q 105

Determine where is the angle between u and v. Round answer to two decimal places.
A) 10.61
B) 10.25
C) 7.50
D) 9.05
E) 12.99

Free

Multiple Choice

Q 106Q 106

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 114Q 114

Find the standard form of the complex number shown below. Round answers to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 115Q 115

Find the standard form of the complex number . Round values to the nearest hundredth.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 116Q 116

Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 117Q 117

Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 118Q 118

Divide the complex numbers below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 119Q 119

Find the product using trigonometric forms. Leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 120Q 120

Use DeMoivre's Theorem to find the indicated power of the following complex number.
A) -324
B) 729
C) 324
D) 2,916
E) 243

Free

Multiple Choice

Q 121Q 121

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 122Q 122

Use DeMoivre's Theorem to find the indicated power of the following complex number.
A) 32
B) 64
C)
D)
E) -64

Free

Multiple Choice

Free

Multiple Choice

Q 124Q 124

Find the cube roots of the following complex number. Write each of the roots in standard form.
A) , ,
B) ,
C)
D) , ,
E) , ,

Free

Multiple Choice

Free

Multiple Choice

Q 126Q 126

Given that Force 1 = 70 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 90 pounds. Round answer to the nearest degree.
A) 60°
B) 40°
C) 53°
D) 45°
E) 48°

Free

Multiple Choice

Q 127Q 127

Given vectors and determine the quantity indicated below.
A) -12
B) -180
C) 10
D) 60
E) -70

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 130Q 130

Determine where is the angle between u and v. Round answer to two decimal places.
A) 10.61
B) 10.25
C) 7.50
D) 9.05
E) 12.99

Free

Multiple Choice

Q 131Q 131

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 139Q 139

Find the standard form of the complex number shown below. Round answers to two decimal places.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 140Q 140

Find the standard form of the complex number . Round values to the nearest hundredth.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 141Q 141

Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 142Q 142

Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 143Q 143

Divide the complex numbers below and leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 144Q 144

Find the product using trigonometric forms. Leave the result in trigonometric form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 145Q 145

Use DeMoivre's Theorem to find the indicated power of the following complex number.
A) -324
B) 729
C) 324
D) 2,916
E) 243

Free

Multiple Choice

Q 146Q 146

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 147Q 147

Use DeMoivre's Theorem to find the indicated power of the following complex number.
A) 32
B) 64
C)
D)
E) -64

Free

Multiple Choice

Free

Multiple Choice

Q 149Q 149

Find the cube roots of the following complex number. Write each of the roots in standard form.
A) , ,
B) ,
C)
D) , ,
E) , ,

Free

Multiple Choice

Free

Multiple Choice