Deck 6: Additional Topics in Trigonometry

Question 1

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

Answer 1

A

Question 2

Answer 2

D

Question 3

Use the figure to determine the tension in the cable CA supporting the load. Round your answer to two decimals.

A) 3194.44 lbs.
B) 9996.76 lbs.
C) 6881.42 lbs.
D) 2500.81 lbs.
E) 3632.97 lbs.

Answer 3

D

Question 4

Question 5

Question 6

Question 7

Question 8

Find all solutions to the following equation.

Question 9

Question 10

Question 11

Given a = 5 , b = 9 , and c =12 , use Heron's Area Formula to find the area of triangle ABC . Round answer to two decimal places.

A) 20.40 sq. units
B) 16.97 sq. units
C) 19.60 sq. units
D) 12.65 sq. units
E) 17.40 sq. units

Question 12

Question 13

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

A) 1,953,125
B) 390,625
C) 78,125
D) 1,000,000
E) 3,125

Question 14

Question 15

Question 16

A) 60.33°
B) 76.53°
C) 40.42°
D) 80.44°
E) 63.06°

Question 17

Question 18

Question 19

Plot the following complex number.

Question 20

A) -216
B) -240
C) 68
D) -48
E) 4

Question 21

Question 22

Question 23

Question 24

A plane flies 740 miles from City A to City B with a bearing of 25° (clockwise from north). Then it flies 614 miles from City B to City C with a bearing of 49°. Find the
Straight-line distance from City C to City A. Round your answer to two decimals.

A) 307.31 miles
B) 1347.06 miles
C) 1137.63 miles
D) 911.87 miles
E) 1324.67 miles

Question 25

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

A) 37.44 sq. units
B) 33.70 sq. units
C) 29.95 sq. units
D) 44.93 sq. units
E) 41.19 sq. units

Question 26

A) orthogonal
B) parallel
C) neither

Question 27

Question 28

Question 29

A boat race runs along a triangular course marked by buoys A, B, and C. The race begins with the boats headed west for 3900 meters. The other two sides of the course
Lie to the north of the first side, and their lengths are 1900 meters and 2500 meters,
Respectively. Find the bearing for the last leg of the race. Round your answer to two
Decimals.

A) -inf°
B) 113.74°
C) 180.01°
D) 156.26°
E) 90.01°

Question 30

Question 31

Question 32

Question 33

A) orthogonal
B) parallel
C) neither

Question 34

Question 35

Question 36

Question 37

Question 38

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 5° from vertical toward the house.
From the porch, which is 100 feet away from the base of the tree, they noticed that the
Angle of elevation to the top of the tree was 29°. Approximate the height of the tree.
Round answer to two decimal places.

A) 57.19 feet
B) 58.48 feet
C) 68.48 feet
D) 53.07 feet
E) 60.01 feet

Question 39

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
128Ab=°, =8, and c=15

A) 56.74 sq. units
B) 47.28 sq. units
C) 37.82 sq. units
D) 42.55 sq. units
E) 52.01 sq. units

Question 40

Question 41

A) 5.47 feet
B) 6.22 feet
C) 10.28 feet
D) 13.86 feet
E) 5.94 feet

Question 42

Question 43

A) 4.47 miles
B) 4.72 miles
C) 7.98 miles
D) 7.07 miles
E) 7.47 miles

Question 44

Question 45

Question 46

A) orthogonal
B) parallel
C) neither

Question 47

A 400 -pound trailer is sitting on an exit ramp inclined at 31° 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) 206.02 pounds
B) 342.87 pounds
C) 274.44 pounds
D) 308.65 pounds
E) 325.76 pounds

Question 48

Question 49

Given A =°16 , b =12 , and a = 10 , 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) c =18.62
B) c = 2.10 and 20.97
C) c =19.75
D) c =1.12 and 17.85
E) not possible

Question 50

A) 20
B) 2
C) 16
D) 24
E) 18

Question 51

A) 92.52
B) 94.61°
C) 95.95
D) 93.42
E) 97.13°

Question 52

Question 53

Question 54

Question 55

Question 56

A) ()2, -1
B) ()12,9
C) ()0,1
D) ()9,12
E) ()10,11

Question 57

A) 46.34 sq. units
B) 38.61 sq. units
C) 30.89 sq. units
D) 34.75 sq. units
E) 42.47 sq. units

Question 58

Question 59

Question 60

Question 61

Question 62

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

A) 89.40 sq. units
B) 67.05 sq. units
C) 59.60 sq. units
D) 74.50 sq. units
E) 81.95 sq. units

Question 63

A plane flies 440 kilometers with a bearing of 320° from City A to City B (see figure below). The plane then flies 800 kilometers from City B to City C, which is directly
West of City A. Find the bearing of the flight from City B to City C. Round your
Answer to two decimals.

A) 245.08°
B) 335.08°
C) 24.92°
D) 20.70°
E) 249.30°

Question 64

A) 7.14
B) 13.62
C) 15.78
D) 12.00
E) 11.46

Question 65

Question 66

A) orthogonal
B) parallel
C) neither

Question 67

Question 68

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

A) orthogonal
B) parallel
C) neither

Question 69

Question 70

A triangular parcel of land has sides of lengths 900, 580, and 550 feet. Approximate the area of the land. Round answer to nearest foot.

Question 71

Question 72

Question 73

Given a =13, b = 11, and c = 6 , use Heron's Area Formula to find the area of triangle ABC . Round answer to two decimal places.

A) 32.86 sq. units
B) 28.14 sq. units
C) 20.78 sq. units
D) 30.59 sq. units
E) 28.10 sq. units

Question 74

Question 75

Question 76

Question 77

Find the vector v that has a magnitude of 4 and is in the same direction as u, where

Question 78

Question 79

Question 80

A) I is the only root.
B) None are roots.
C) III is the only root.
D) I and II are the only roots.
E) I and III are the only roots.