Deck 8: Additional Topics in Trigonometry

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

A park ranger at point A observes a fire in the direction . Another ranger at point B, 5 miles due east of A, sites the same fire at . Determine the distance from point B to the fire. Round answer to two decimal places.

A) 2.18 miles
B) 4.55 miles
C) 2.51 miles
D) 4.84 miles
E) 4.20 miles

Answer 2

4.55 miles

Question 3

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

A) 30.90 sq. units
B) 37.08 sq. units
C) 33.99 sq. units
D) 27.81 sq. units
E) 24.72 sq. units

Answer 3

30.90 sq. units

Question 4

Find the component form of vector v.

A)
B)
C)
D)
E)

Question 5

A vertical pole 29 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 78 feet downhill from the base of the pole. Round answer to two decimal places.

A) 82.88 feet
B) 75.35 feet
C) 99.45 feet
D) 88.40 feet
E) feet

Question 6

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 98 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) 47.99 feet
B) 56.03 feet
C) 41.91 feet
D) 45.31 feet
E) 46.03 feet

Question 7

final If and , and the vectors make angles of 0° and 60° and 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 8

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of at 15 miles per hour, and the other travels at a bearing of at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

A) 44.71 miles
B) 23.86 miles
C) 30.37 miles
D) 27.02 miles
E) 39.96 miles

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) a= 8.37
B) a= 10.02
C) a= 5.92
D) a= 21.05
E) a= 7.14

Question 10

Find the magnitude and direction angle of .

A)
B)
C)
D)
E)

Question 11

Find the component form of v if and the angle it makes with the x-axis is 150°.

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) 28.61 sq. units
B) 23.84 sq. units
C) 21.46 sq. units
D) 26.22 sq. units
E) 19.07 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) 16.29
B) 11.26
C) 15.57
D) 17.00
E) 14.13

Question 14

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

A) 59.30 sq. units
B) 88.95 sq. units
C) 66.71 sq. units
D) 81.54 sq. units
E) 74.13 sq. units

Question 15

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

A)
B)
C)
D)
E)

Question 16

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

A)
B)
C)
D)
E)

Question 17

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

A)
B)
C)
D)
E)

Question 18

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

A) 17.36 sq. units
B) 18.44 sq. units
C) 20.21 sq. units
D) 16.76 sq. units
E) 14.02 sq. units

Question 19

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

A) a= 14.57
B) a= 13.14
C) a= 11.24
D) a= 13.69
E) a= 12.46

Question 20

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) 4.78 feet
B) 9.04 feet
C) 7.08 feet
D) 12.32 feet
E) 5.87 feet

Question 21

A 725-pound trailer is sitting on an exit ramp inclined at 36° 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) 566.49 pounds
B) 546.44 pounds
C) 586.54 pounds
D) 506.34 pounds
E) 426.14 pounds

Question 22

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

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

Question 23

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

A) neither
B) parallel
C) orthogonal

Question 24

Divide the complex numbers below and leave the result in trigonometric form.

A)
B)
C)
D)
E)

Question 25

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

A)
B)
C)
D)
E)

Question 26

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

A)
B)
C)
D)
E)

Question 27

Find the trigonometric form of .

A)
B)
C)
D)
E)

Question 28

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 23 feet. How much work has been accomplished? Round answer to one decimal place.

A) 965.7 foot-pounds
B) 1,035.0 foot-pounds
C) 1,195.1 foot-pounds
D) 896.3 foot-pounds
E) 1,080.4 foot-pounds

Question 29

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

A)
B)
C)
D)
E)

Question 30

Multiply the complex numbers below and leave the result in trigonometric form.

A)
B)
C)
D)
E)

Question 31

Multiply the complex numbers below and leave the result in trigonometric form.

A)
B)
C)
D)
E)

Question 32

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

A)
B)
C)
D)
E)

Question 33

Find the product using trigonometric forms. Leave the result in trigonometric form.

A)
B)
C)
D)
E)

Question 34

Find the standard form of the complex number . Round values to the nearest hundredth.

A)
B)
C)
D)
E)

Question 35

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 5.5%.

A) $10,701,150
B) $10,852,400
C) $11,003,650
D) $10,732,500
E) $10,812,433

Question 36

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

A) neither
B) orthogonal
C) parallel

Question 37

Find the standard form of the complex number shown below.

A)
B)
C)
D)
E)

Question 38

Find the projection of u onto v if , .

A)
B)
C)
D)
E)

Question 39

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

A) 3,125
B) 62,500
C) 15,625
D) 2,500
E) -2,500

Question 40

Find the trigonometric form of .

A)
B)
C)
D)
E)

Question 41

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

A)
B)
C)
D)
E)

Question 42

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

A) 2048
B)
C) -4,096
D)
E) 4,096