Deck 7: Additional Topics in Trigonometry

Question 1

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)

Answer 1

Question 2

In the figure below, , , and . Use this information to solve the parallelogram for $\beta$ . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the magnitude of vector v.

A)
B)
C)
D)
E)

Answer 3

Question 4

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)

Question 5

Given and , determine .

A)
B)
C)
D)
E)

Question 6

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)

Question 7

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

Question 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)

Question 9

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)

Question 10

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

Question 11

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)

Question 12

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

Question 13

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)

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

Given and , determine .

A)
B)
C)
D)
E)

Question 19

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

Question 20

Find the magnitude of vector v with initial point and terminal point .

A)
B)
C)
D)
E)

Question 21

Find the vector v that has a magnitude of and is in the same direction as u, where .

A)
B)
C)
D)
E)

Question 22

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

Question 23

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)

Question 24

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

Question 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)

Question 26

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

Question 27

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

Question 28

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

Question 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

Question 30

Find the component form of v if and the angle it makes with the x-axis is .

A)
B)
C)
D)
E)

Question 31

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

Question 32

In the figure below, , , and . Use this information to solve the parallelogram for F $\beta$ . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 33

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)

Question 34

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)

Question 35

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)

Question 36

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)

Question 37

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)

Question 38

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

Question 39

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)

Question 40

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)

Question 41

Given and , determine .

A)
B)
C)
D)
E)

Question 42

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)

Question 43

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

Question 44

Find the magnitude of vector v with initial point and terminal point .

A)
B)
C)
D)
E)

Question 45

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)

Question 46

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)

Question 47

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

Question 48

Find the component form of v if and the angle it makes with the x-axis is .

A)
B)
C)
D)
E)

Question 49

Find the vector v that has a magnitude of and is in the same direction as u, where .

A)
B)
C)
D)
E)

Question 50

Given and , determine .

A)
B)
C)
D)
E)

Question 51

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

Question 52

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)

Question 53

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)

Question 54

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)

Question 55

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

Question 56

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

Question 57

Find the magnitude of vector v.

A)
B)
C)
D)
E)

Question 58

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)

Question 59

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

Question 60

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)

Question 61

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

Question 62

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

Question 63

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)

Question 64

In the figure below, , , and . Use this information to solve the parallelogram for $\beta$ . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 65

Given vectors and determine the quantity indicated below.

A) -6
B) -21
C) 36
D) -18
E) 78

Question 66

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

Question 67

Given and , determine .

A)
B)
C)
D)
E)

Question 68

Find the vector v that has a magnitude of and is in the same direction as u, where .

A)
B)
C)
D)
E)

Question 69

Find the component form of v if and the angle it makes with the x-axis is .

A)
B)
C)
D)
E)

Question 70

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)

Question 71

Given and , determine .

A)
B)
C)
D)
E)

Question 72

Find the angle between the vectors u and v.

A)
B)
C)
D)
E)

Question 73

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)

Question 74

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)

Question 75

Determine where $\theta$ 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

Question 76

Find the magnitude of vector v.

A)
B)
C)
D)
E)

Question 77

Find the magnitude of vector v with initial point and terminal point .

A)
B)
C)
D)
E)

Question 78

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

Question 79

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°

Question 80

Use the dot product to find the magnitude of u if

A)
B)
C)
D)
E)