Question 1

Find u - v. ​   ​

Accepted Answer

A) ​-i - 4j 
B) -2i - 4j 
C) -i + 4j 
D) -2i + 4j 
E) -i + 5j 
A) ​-i - 4j 
B) -2i - 4j 
C) -i + 4j 
D) -2i + 4j 
E) -i + 5j

Question 2

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. ​
​   ​
Where b = 28°
​

Accepted Answer

A) 18.0 lb 
B) 17.0 lb 
C) 16.0 lb 
D) 19.0 lb 
E) 15.0 lb 
A) 18.0 lb 
B) 17.0 lb 
C) 16.0 lb 
D) 19.0 lb 
E) 15.0 lb

Question 3

A vertical pole 29 feet tall stands on a hillside that makes an angle of 20° with the horizontal.Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 65 feet downhill from the base of the pole.Round your answer to two decimal places. ​

Accepted Answer

A) 70.59 feet 
B) 61.45 feet 
C) 84.70 feet 
D) 75.29 feet 
E) 79.72 feet 
A) 70.59 feet 
B) 61.45 feet 
C) 84.70 feet 
D) 75.29 feet 
E) 79.72 feet

Question 4

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 3° from vertical toward the house.From the porch, which is 96 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was 31°.Approximate the height of the tree.Round answer to two decimal places. ​

Accepted Answer

A) 61.76 feet 
B) 69.64 feet 
C) 56 feet 
D) 59.13 feet 
E) 59.64 feet 
A) 61.76 feet 
B) 69.64 feet 
C) 56 feet 
D) 59.13 feet 
E) 59.64 feet

Question 5

Find u + v. ​   ​

Accepted Answer

A) ​   
B)    
C) ​   
D) ​   
E) ​   
A) ​   
B)    
C) ​   
D) ​   
E) ​

Question 6

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ1 = 40° and θ2 = 35°.Approximate the answers to one decimal place. ​   ​

Accepted Answer

A) ​​TL = 12.7 lb; TR = 12.7 lb 
B) ​TL = 11.9 lb; TR = 11.9 lb 
C) ​TL = 11.9 lb; TR = 12.7 lb 
D) TL = 12.7 lb; TR = 11.9 lb 
E) ​​TL = 13.7 lb; TR = 12.9 lb 
A) ​​TL = 12.7 lb; TR = 12.7 lb 
B) ​TL = 11.9 lb; TR = 11.9 lb 
C) ​TL = 11.9 lb; TR = 12.7 lb 
D) TL = 12.7 lb; TR = 11.9 lb 
E) ​​TL = 13.7 lb; TR = 12.9 lb

Question 7

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 51, b = 21, c = 68
​

Accepted Answer

A) A ≈ 30.37°, B ≈ 12.02°, C ≈ 137.61° 
B) A ≈ 30.37°, B ≈ 137.61°, C ≈ 12.02° 
C) A ≈ 12.02°, B ≈ 30.37°, C ≈ 137.61° 
D) A ≈ 137.61°, B ≈ 12.02°, C ≈ 30.37° 
E) A ≈ 137.61°, B ≈ 30.37°, C ≈ 12.02° 
A) A ≈ 30.37°, B ≈ 12.02°, C ≈ 137.61° 
B) A ≈ 30.37°, B ≈ 137.61°, C ≈ 12.02° 
C) A ≈ 12.02°, B ≈ 30.37°, C ≈ 137.61° 
D) A ≈ 137.61°, B ≈ 12.02°, C ≈ 30.37° 
E) A ≈ 137.61°, B ≈ 30.37°, C ≈ 12.02°

Question 8

Given a = 8, b = 14, and c = 12, use the Law of Cosines to solve the triangle for the value of C.Round your answer to two decimal places. ​

Accepted Answer

A) 60.33° 
B) 86.42° 
C) 58.81° 
D) 34.77° 
E) 80.44° 
A) 60.33° 
B) 86.42° 
C) 58.81° 
D) 34.77° 
E) 80.44°

Question 9

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

Accepted Answer

A) 69.48° 
B) 71.57° 
C) 72.91° 
D) 70.38° 
E) 74.09° 
A) 69.48° 
B) 71.57° 
C) 72.91° 
D) 70.38° 
E) 74.09°

Question 10

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​
Magnitude
Angle   0°
​
​

Accepted Answer

A)    
B) ​   
C) ​   
D) ​   
E) ​   
A)    
B) ​   
C) ​   
D) ​   
E) ​

Question 11

Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 12

A force of   pounds exerted at an angle of   above the horizontal is required to slide a table across a floor (see figure).The table is dragged   feet.Determine the work done in sliding the table. ​   ​

Accepted Answer

A) 539.6 ft-lb 
B) 599.6 ft-lb 
C) 519.6 ft-lb 
D) 579.6 ft-lb 
E) 559.6 ft-lb 
A) 539.6 ft-lb 
B) 599.6 ft-lb 
C) 519.6 ft-lb 
D) 579.6 ft-lb 
E) 559.6 ft-lb

Question 13

Find the dot product of u and v. ​   ​

Accepted Answer

A) 14 
B) 6 
C) 12 
D) 10 
E) 8 
A) 14 
B) 6 
C) 12 
D) 10 
E) 8

Question 14

Given   and   , find   .

Accepted Answer

A) -10 
B) -14 
C) 11 
D) -5 
E) -12 
A) -10 
B) -14 
C) 11 
D) -5 
E) -12

Question 15

You want to buy a triangular lot measuring 500 yards by 830 yards by 1110 yards.The price of the land is $2000 per acre.How much does the land cost? (Hint: 1 acre = 4840 square yards)
​

Accepted Answer

A) $80,335.71 
B) $80,465.71 
C) $80,415.71 
D) $80,315.71 
E) $80,215.71 
A) $80,335.71 
B) $80,465.71 
C) $80,415.71 
D) $80,315.71 
E) $80,215.71

Question 16

Find the area of the triangle having the indicated angle and sides. ​
С = 84°34', a = 16, b = 26
​
(Round your answer to one decimal place.)
​

Accepted Answer

A) 209.1 
B) ​207.1 
C) ​208.1 
D) ​206.1 
E) ​414.1 
A) 209.1 
B) ​207.1 
C) ​208.1 
D) ​206.1 
E) ​414.1

Question 17

Find the dot product of u and v. ​   ​

Accepted Answer

A) 18 
B) 14 
C) 20 
D) 12 
E) 16 
A) 18 
B) 14 
C) 20 
D) 12 
E) 16

Question 18

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%.

Accepted Answer

A) ​1.06(u + v) 
B) 1.06   
C)    
D) 1.06   
E) 1.06   
A) ​1.06(u + v) 
B) 1.06   
C)    
D) 1.06   
E) 1.06

Question 19

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. ​
A = 18, b = 20, C = 65°
​

Accepted Answer

A) Law of Sines; A ≈ 65°, B ≈ 52.79°, c ≈ 20 
B) Law of Sines; A ≈ 52.79°, B ≈ 65°, c ≈ 20 
C) Law of Cosines; A ≈ 52.79°, B ≈ 62.21°, c ≈ 20.49 
D) Law of Sines; No solution 
E) Law of Cosines; No solution 
A) Law of Sines; A ≈ 65°, B ≈ 52.79°, c ≈ 20 
B) Law of Sines; A ≈ 52.79°, B ≈ 65°, c ≈ 20 
C) Law of Cosines; A ≈ 52.79°, B ≈ 62.21°, c ≈ 20.49 
D) Law of Sines; No solution 
E) Law of Cosines; No solution

Question 20

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 73   , a = 12.5 and b = 11.5
​

Accepted Answer

A) 68.96 sq.units 
B) 62.06 sq.units 
C) 55.17 sq.units 
D) 82.75 sq.units 
E) 75.85 sq.units 
A) 68.96 sq.units 
B) 62.06 sq.units 
C) 55.17 sq.units 
D) 82.75 sq.units 
E) 75.85 sq.units

Find u - v.

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. Where b = 28°

A vertical pole 29 feet tall stands on a hillside that makes an angle of 20° with the horizontal.Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 65 feet downhill from the base of the pole.Round your answer to two decimal places.

Find u + v.

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place.

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 51, b = 21, c = 68

Given a = 8, b = 14, and c = 12, use the Law of Cosines to solve the triangle for the value of C.Round your answer to two decimal places.

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

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle 0°

Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.

A force of pounds exerted at an angle of above the horizontal is required to slide a table across a floor (see figure).The table is dragged feet.Determine the work done in sliding the table.

Find the dot product of u and v.

Given and , find .

You want to buy a triangular lot measuring 500 yards by 830 yards by 1110 yards.The price of the land is $2000 per acre.How much does the land cost? (Hint: 1 acre = 4840 square yards)

Find the area of the triangle having the indicated angle and sides. С = 84°34', a = 16, b = 26 (Round your answer to one decimal place.)

Find the dot product of u and v.

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%.

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. A = 18, b = 20, C = 65°

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 73 , a = 12.5 and b = 11.5

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

Find u - v. ​ ​

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. ​ ​ ​ Where b = 28° ​

A vertical pole 29 feet tall stands on a hillside that makes an angle of 20° with the horizontal.Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 65 feet downhill from the base of the pole.Round your answer to two decimal places. ​

Find u + v. ​ ​

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ1 = 40° and θ2 = 35°.Approximate the answers to one decimal place. ​ ​

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 51, b = 21, c = 68 ​

Given a = 8, b = 14, and c = 12, use the Law of Cosines to solve the triangle for the value of C.Round your answer to two decimal places. ​

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

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​ Magnitude Angle 0° ​ ​

Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.

A force of pounds exerted at an angle of above the horizontal is required to slide a table across a floor (see figure).The table is dragged feet.Determine the work done in sliding the table. ​ ​

Find the dot product of u and v. ​ ​

Given and , find .

You want to buy a triangular lot measuring 500 yards by 830 yards by 1110 yards.The price of the land is $2000 per acre.How much does the land cost? (Hint: 1 acre = 4840 square yards) ​

Find the area of the triangle having the indicated angle and sides. ​ С = 84°34', a = 16, b = 26 ​ (Round your answer to one decimal place.) ​

Find the dot product of u and v. ​ ​

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%.

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. ​ A = 18, b = 20, C = 65° ​

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 73 , a = 12.5 and b = 11.5 ​

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find u - v.

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. Where b = 28°

A vertical pole 29 feet tall stands on a hillside that makes an angle of 20° with the horizontal.Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 65 feet downhill from the base of the pole.Round your answer to two decimal places.

Find u + v.

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place.

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 51, b = 21, c = 68

Given a = 8, b = 14, and c = 12, use the Law of Cosines to solve the triangle for the value of C.Round your answer to two decimal places.

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle 0°

A force of pounds exerted at an angle of above the horizontal is required to slide a table across a floor (see figure).The table is dragged feet.Determine the work done in sliding the table.

Find the dot product of u and v.

You want to buy a triangular lot measuring 500 yards by 830 yards by 1110 yards.The price of the land is $2000 per acre.How much does the land cost? (Hint: 1 acre = 4840 square yards)

Find the area of the triangle having the indicated angle and sides. С = 84°34', a = 16, b = 26 (Round your answer to one decimal place.)

Find the dot product of u and v.

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. A = 18, b = 20, C = 65°

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 73 , a = 12.5 and b = 11.5