Question 1

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129°, b = 8, and c = 11

Accepted Answer

A) 34.19 sq.units 
B) 41.03 sq.units 
C) 37.61 sq.units 
D) 30.77 sq.units 
E) 27.36 sq.units 
A) 34.19 sq.units 
B) 41.03 sq.units 
C) 37.61 sq.units 
D) 30.77 sq.units 
E) 27.36 sq.units

Question 2

A tractor pulls a log 900 meters, and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is   above the horizontal.Approximate the work done in pulling the log. ​
(Round the answer to two decimal places.)
​

Accepted Answer

A) 12,305,260.09 N-m 
B) 12,305,220.09 N-m 
C) 12,305,300.09 N-m 
D) 12,305,280.090 N-m 
E) 12,305,240.09 N-m 
A) 12,305,260.09 N-m 
B) 12,305,220.09 N-m 
C) 12,305,300.09 N-m 
D) 12,305,280.090 N-m 
E) 12,305,240.09 N-m

Question 3

Find values for b such that the triangle has one solution. ​
A = 44°, a = 6
​

Accepted Answer

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

Question 4

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 3.5%.

Accepted Answer

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

Question 5

Find the dot product of u and v. ​   ​

Accepted Answer

A) -31 
B) -29 
C) -33 
D) -37 
E) -35 
A) -31 
B) -29 
C) -33 
D) -37 
E) -35

Question 6

Given a = 10, b = 14, and c = 9, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places.   Figure not drawn to scale

Accepted Answer

A) 94.78° 
B) 80.44° 
C) 39.84° 
D) 45.38° 
E) 60.33° 
A) 94.78° 
B) 80.44° 
C) 39.84° 
D) 45.38° 
E) 60.33°

Question 7

A loaded barge is being towed by two tugboats, and the magnitude of the resultant is 6,400 pounds directed along the axis of the barge (see figure).Find the tension in the tow lines if they each make an angle 21° with the axis of the barge.Approximate the answer to one decimal place. ​   ​
Where a = 21°.

Accepted Answer

A) 3,425.7 lb 
B) 3,429.7 lb 
C) 3,426.7 lb 
D) 3,428.7 lb 
E) 3,427.7 lb 
A) 3,425.7 lb 
B) 3,429.7 lb 
C) 3,426.7 lb 
D) 3,428.7 lb 
E) 3,427.7 lb

Question 8

Given vectors   and   determine the quantity indicated below.

Accepted Answer

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

Question 9

Find a unit vector in the direction of the given vector. ​   ​

Accepted Answer

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

Question 10

Use the dot product to find the magnitude of u if

Accepted Answer

A)    10 
B)      
C)    
D)    
E)      
A)    10 
B)      
C)    
D)    
E)

Question 11

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​
A = 60°, a = 13, b = 11.6
​

Accepted Answer

A) B ≈ 69.40°, C ≈ 50.6°, c ≈ 11.6 
B) B ≈ 91°, C ≈ 29°, c ≈ 14.05 
C) B ≈ 50.6°, C ≈ 69.40°, c ≈ 14.05 
D) B ≈ 29°, C ≈ 91°, c ≈ 13 
E) No Solution 
A) B ≈ 69.40°, C ≈ 50.6°, c ≈ 11.6 
B) B ≈ 91°, C ≈ 29°, c ≈ 14.05 
C) B ≈ 50.6°, C ≈ 69.40°, c ≈ 14.05 
D) B ≈ 29°, C ≈ 91°, c ≈ 13 
E) No Solution

Question 12

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places.   ​ a = 8, b = 10, c = 14
​

Accepted Answer

A) A ≈ 101.53°, B ≈ 44.42°, C ≈ 34.05° 
B) A ≈ 34.05°, B ≈ 101.53°, C ≈ 44.42° 
C) A ≈ 44.42°, B ≈ 44.42°, C ≈ 91.16° 
D) A ≈ 44.42°, B ≈ 34.05°, C ≈ 101.53° 
E) A ≈ 34.05°, B ≈ 44.42°, C ≈ 101.53° 
A) A ≈ 101.53°, B ≈ 44.42°, C ≈ 34.05° 
B) A ≈ 34.05°, B ≈ 101.53°, C ≈ 44.42° 
C) A ≈ 44.42°, B ≈ 44.42°, C ≈ 91.16° 
D) A ≈ 44.42°, B ≈ 34.05°, C ≈ 101.53° 
E) A ≈ 34.05°, B ≈ 44.42°, C ≈ 101.53°

Question 13

Find values for b such that the triangle has one solution. ​
A = 74°, a = 17
​

Accepted Answer

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

Question 14

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet)
​

Accepted Answer

A) $63,450.91 
B) $63,300.91 
C) $63,400.91 
D) $63,200.91 
E) $63,320.91 
A) $63,450.91 
B) $63,300.91 
C) $63,400.91 
D) $63,200.91 
E) $63,320.91

Question 15

Find the projection of u onto v if   ,   . ​

Accepted Answer

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

Question 16

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

Accepted Answer

A) 36.87° 
B) 37.83° 
C) 38.28° 
D) 34.94° 
E) 35.63° 
A) 36.87° 
B) 37.83° 
C) 38.28° 
D) 34.94° 
E) 35.63°

Question 17

Find values for b such that the triangle has one solution. ​
A = 62°, a = 304.6
​

Accepted Answer

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

Question 18

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.) ​

Accepted Answer

A) Vertical ≈ -55.7 mi/h, Horisontal ≈ 91.7 mi/h. 
B) Vertical ≈ 90.7 mi/h, Horisontal ≈ -56.7 mi/h. 
C) Vertical ≈ -56.7 mi/h, Horisontal ≈ -56.7 mi/h. 
D) Vertical ≈ -56.7 mi/h, Horisontal ≈ 90.7 mi/h. 
E) Vertical ≈ 90.7 mi/h, Horisontal ≈ 90.7 mi/h. 
A) Vertical ≈ -55.7 mi/h, Horisontal ≈ 91.7 mi/h. 
B) Vertical ≈ 90.7 mi/h, Horisontal ≈ -56.7 mi/h. 
C) Vertical ≈ -56.7 mi/h, Horisontal ≈ -56.7 mi/h. 
D) Vertical ≈ -56.7 mi/h, Horisontal ≈ 90.7 mi/h. 
E) Vertical ≈ 90.7 mi/h, Horisontal ≈ 90.7 mi/h.

Question 19

Find values for b such that the triangle has no solutions. ​
A = 64°, a = 340.2
​

Accepted Answer

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

Question 20

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​
A = 3.2, b = 10.9, c = 9
​

Accepted Answer

A) 7.0 
B) 6.4 
C) 3.7 
D) 45.3 
E) 12.6 
A) 7.0 
B) 6.4 
C) 3.7 
D) 45.3 
E) 12.6

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129°, b = 8, and c = 11

A tractor pulls a log 900 meters, and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is above the horizontal.Approximate the work done in pulling the log. (Round the answer to two decimal places.)

Find values for b such that the triangle has one solution. A = 44°, a = 6

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 3.5%.

Find the dot product of u and v.

Given a = 10, b = 14, and c = 9, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. Figure not drawn to scale

Given vectors and determine the quantity indicated below.

Find a unit vector in the direction of the given vector.

Use the dot product to find the magnitude of u if

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. A = 60°, a = 13, b = 11.6

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. a = 8, b = 10, c = 14

Find values for b such that the triangle has one solution. A = 74°, a = 17

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet)

Find the projection of u onto v if , .

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

Find values for b such that the triangle has one solution. A = 62°, a = 304.6

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.)

Find values for b such that the triangle has no solutions. A = 64°, a = 340.2

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. A = 3.2, b = 10.9, c = 9

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129°, b = 8, and c = 11

A tractor pulls a log 900 meters, and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is above the horizontal.Approximate the work done in pulling the log. ​ (Round the answer to two decimal places.) ​

Find values for b such that the triangle has one solution. ​ A = 44°, a = 6 ​

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 3.5%.

Find the dot product of u and v. ​ ​

Given a = 10, b = 14, and c = 9, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. Figure not drawn to scale

Given vectors and determine the quantity indicated below.

Find a unit vector in the direction of the given vector. ​ ​

Use the dot product to find the magnitude of u if

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​ A = 60°, a = 13, b = 11.6 ​

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ a = 8, b = 10, c = 14 ​

Find values for b such that the triangle has one solution. ​ A = 74°, a = 17 ​

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet) ​

Find the projection of u onto v if , . ​

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

Find values for b such that the triangle has one solution. ​ A = 62°, a = 304.6 ​

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.) ​

Find values for b such that the triangle has no solutions. ​ A = 64°, a = 340.2 ​

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​ A = 3.2, b = 10.9, c = 9 ​

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

A tractor pulls a log 900 meters, and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is above the horizontal.Approximate the work done in pulling the log. (Round the answer to two decimal places.)

Find values for b such that the triangle has one solution. A = 44°, a = 6

Find the dot product of u and v.

Find a unit vector in the direction of the given vector.

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. A = 60°, a = 13, b = 11.6

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. a = 8, b = 10, c = 14

Find values for b such that the triangle has one solution. A = 74°, a = 17

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet)

Find the projection of u onto v if , .

Find values for b such that the triangle has one solution. A = 62°, a = 304.6

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.)

Find values for b such that the triangle has no solutions. A = 64°, a = 340.2

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. A = 3.2, b = 10.9, c = 9