Deck 14: Additional Topics in Trigonometry

Question 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)

Answer 1

Question 2

Determine a value for b such that a triangle with and has no solution. Round your answer to the nearest hundredth.

A)
B)
C)
D)
E)

Answer 2

Question 3

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)

Answer 3

Question 4

Given , , and , use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 5

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 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)

Question 7

Given , , and , use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 8

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.

A) sq. units
B) sq. units
C) sq. units
D) sq. units
E) sq. units

Question 9

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.

A) sq. units
B) sq. units
C) sq. units
D) sq. units
E) sq. units

Question 10

Given , , and , 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 11

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 12

Given , , and , use the Law of Sines to solve the triangle (if possible) for the value of b. If two solutions exist, find both. Round answer to two decimal places.

A)
B)
C)
D)
E)not possible

Question 13

Determine a value for b such that a triangle with and has two solutions.

A)
B)
C)
D)
E)

Question 14

Given , , and , use the Law of Sines to solve the triangle (if possible) for the value of b. If two solutions exist, find both. Round answer to two decimal places.

A)
B)
C)
D)
E)not possible

Question 15

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 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.

A) feet
B) feet
C) feet
D) feet
E) feet

Question 16

Determine a value for b such that a triangle with and has only one solution.

A)
B)
C)
D)
E)

Question 17

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 18

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 19

After a severe storm, three sisters, April, May, and June, stood on their front porch and noticed that the tree in their front yard was leaning from vertical toward the house. From the porch, which is feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was . Approximate the height of the tree. Round answer to two decimal places.

A) feet
B) feet
C) feet
D) feet
E) feet

Question 20

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.

A) sq. units
B) sq. units
C) sq. units
D) sq. units
E) sq. units

Question 21

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 22

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)
E)none of these

Question 23

Given and , determine .

A)
B)
C)
D)
E)

Question 24

A vertical pole 37 feet tall stands on a hillside that makes an angle of with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 61 feet downhill from the base of the pole. Round answer to two decimal places.

A) feet
B)84.88 feet
C)70.73 feet
D)75.45 feet
E)61.40 feet

Question 25

Find the component form of vector v.

A)
B)
C)
D)
E)

Question 26

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

A)
B)
C)
D)
E)

Question 27

Given , , and , use Heron's Area Formula to find the area of triangle . Round answer to two decimal places.

A) sq. units
B) sq. units
C) sq. units
D) sq. units
E) sq. units

Question 28

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

A)
B)
C)
D)
E)

Question 29

Find the magnitude and direction angle of . Round direction angle to nearest degree.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 30

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of at 11 miles per hour, and the other travels at a bearing of at 13 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

A)16.85 miles
B)33.51 miles
C)22.38 miles
D)18.89 miles
E)29.39 miles

Question 31

Find a unit vector in the direction of .

A)
B)
C)
D)
E)

Question 32

Given , , and , use Heron's Area Formula to find the area of triangle . Round answer to two decimal places.

A) sq. units
B) sq. units
C) sq. units
D) sq. units
E) sq. units

Question 33

Find the magnitude of vector v.

A)
B)
C)
D)
E)

Question 34

Find the magnitude and direction angle of .

A)
B)
C)
D)
E)

Question 35

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

A)
B)
C)
D)
E)

Question 36

If and , find .

A)
B)
C)
D)
E)

Question 37

Find a unit vector in the direction of .

A)
B)
C)
D)
E)

Question 38

Given and , determine .

A)
B)
C)
D)
E)

Question 39

A triangular parcel of land has sides of lengths feet. Approximate the area of the land. Round answer to nearest foot.

A)230,678 ft²
B)230,010 ft²
C)229,462 ft²
D)229,402 ft²
E)229,950 ft²

Question 40

Find the component form of vector v with initial point and terminal point .

A)
B)
C)
D)
E)

Question 41

Find the projection of u onto v if .

A)
B)
C)
D)
E)

Question 42

If and , and the vectors make angles of with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places.

A)
B)
C)
D)
E)

Question 43

Given and , find .

A)
B)
C)
D)
E)

Question 44

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

A)
B)
C)
D)
E)

Question 45

Find the angle between the vectors u and v if and . Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 46

Three forces with magnitudes of pounds, pounds, and pounds act on an object at angles , , and , respectively, with the positive x-axis. Find the magnitude and direction of the resultant force. Round answers to two decimal places.

A) pounds;
B)130.55 pounds;
C) pounds;
D) pounds;
E)130.55 pounds;

Question 47

Find the angle between the vectors u and v if and . Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 48

Use vectors to find the measure of the angle at vertex B of triangle ABC, when . Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 49

Use the dot product to find the magnitude of u if .

A)
B)
C)
D)
E)

Question 50

Given vectors and , determine the quantity indicated below.

A)
B)
C)
D)
E)

Question 51

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

A)
B)
C)
D)
E)

Question 52

Find the angle between the vectors u and v.

A)
B)
C)
D)
E)

Question 53

Given and , find .

A)
B)
C)
D)
E)

Question 54

Determine whether u and v are orthogonal, parallel, or neither.

A)orthogonal
B)parallel
C)neither

Question 55

Given that and , find the angle beween the forces if the magnitude of the resultant force is . Round answer to the nearest degree.

A)
B)
C)
D)
E)

Question 56

Use the dot product to find the magnitude of u if .

A)
B)
C)
D)
E)

Question 57

Determine whether u are v and orthogonal, parallel, or neither.

A)orthogonal
B)parallel
C)neither

Question 58

Determine whether u and v are orthogonal, parallel, or neither.

A)orthogonal
B)parallel
C)neither

Question 59

Given vectors and , determine the quantity indicated below.

A)
B)
C)
D)
E)

Question 60

Determine if , and , where is the angle between u and v. Round answer to two decimal places.

A)
B)
C)
D)
E)

Question 61

Find the absolute value of the complex number .

A)
B)
C)
D)
E)

Question 62

Represent the complex number below graphically.

A)
B)
C)
D)
E)

Question 63

A force of pounds is exerted along a rope attached to a crate at an angle of above the horizontal. The crate is moved feet. How much work has been accomplished? Round answer to one decimal place.

A) foot-pounds
B) foot-pounds
C) foot-pounds
D) foot-pounds
E) foot-pounds

Question 64

Find the trigonometric form of the complex number shown below.

A)
B)
C)
D)
E)

Question 65

Find the standard form of the complex number shown below. Round answers to two decimal places.

A)
B)
C)
D)
E)

Question 66

Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.

A)
B)
C)
D)
E)

Question 67

A -pound trailer is sitting on an exit ramp inclined at on Highway 35. How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

A) pounds
B) pounds
C) pounds
D) pounds
E) pounds

Question 68

Find the trigonometric form of the complex number shown below.

A)
B)
C)
D)
E)

Question 69

Find the trigonometric form of the complex number shown below.

A)
B)
C)
D)
E)

Question 70

Plot the following complex number.

A)
B)
C)
D)
E)

Question 71

Find the trigonometric form of the complex number shown below.

A)
B)
C)
D)
E)

Question 72

Find the trigonometric form of the complex number shown below.

A)
B)
C)
D)
E)

Question 73

Perform the operation shown below and leave the result in trigonometric form.

A)
B)
C)
D)
E)

Question 74

Write the complex number shown below in trigonometric form.

A)
B)
C)
D)
E)

Question 75

Perform the operation shown below and leave the result in trigonometric form.

A)
B)
C)
D)
E)

Question 76

Use DeMoivre's Theorem to find the indicated power of the following complex number.

A)19,683
B)6,561
C)2,187
D)46,656
E)243

Question 77

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. Use dot products to determine the revenue for these two laptops if the price of each is increased by 7%.

A)
B)
C)
D)
E)

Question 78

Graphically represent the following complex number.

A)
B)
C)
D)
E)

Question 79

Find the standard form of the complex number shown below.

A)
B)
C)
D)
E)

Question 80

Perform the operation shown below and leave the result in trigonometric form.

A)
B)
C)
D)
E)