Question 1

​If   and   , find   .

Accepted Answer

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

Question 2

Select a value for b such that a triangle with A = 33° and a = 4 has no solution.

Accepted Answer

A) 1.84 
B) 3.67 
C) 7.24 
D) 14.68 
E) 1.47 
A) 1.84 
B) 3.67 
C) 7.24 
D) 14.68 
E) 1.47

Question 3

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
C = 40°, a =   , b =   ​

Accepted Answer

A) A ≈ 41.21°, B ≈ 98.79°, c ≈ 0.13 
B) A ≈ 99.76°, B ≈ 98.76°, c ≈ 0.13 
C) A ≈ 98.76°, B ≈ 41.24°, c ≈ 0.20 
D) A ≈ 41.24°, B ≈ 98.76°, c ≈ 0.20 
E) A ≈ 98.79°, B ≈ 41.21°, c ≈ 0.20 
A) A ≈ 41.21°, B ≈ 98.79°, c ≈ 0.13 
B) A ≈ 99.76°, B ≈ 98.76°, c ≈ 0.13 
C) A ≈ 98.76°, B ≈ 41.24°, c ≈ 0.20 
D) A ≈ 41.24°, B ≈ 98.76°, c ≈ 0.20 
E) A ≈ 98.79°, B ≈ 41.21°, c ≈ 0.20

Question 4

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

Accepted Answer

A) neither 
B) parallel 
C) orthogonal 
A) neither 
B) parallel 
C) orthogonal

Question 5

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form. ​

Accepted Answer

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

Question 6

Use the dot product to find the magnitude of u if

Accepted Answer

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

Question 7

To approximate the length of a marsh, a surveyor walks 255 meters from point A to point B, then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh. ​   ​
Where a = 225 m, b = 255 m
​

Accepted Answer

A) 365.5 m 
B) 359.5 m 
C) 370.5 m 
D) 371.5 m 
E) 360.5 m 
A) 365.5 m 
B) 359.5 m 
C) 370.5 m 
D) 371.5 m 
E) 360.5 m

Question 8

Find the component form of vector v. ​
​   ​

Accepted Answer

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

Question 9

Find the area of the triangle having the indicated angle and sides. ​
B = 71°20', a = 62, c = 24
​
(Round your answer to one decimal place.)
​

Accepted Answer

A) 705.9 
B) ​703.9 
C) ​706.9 
D) ​704.9 
E) ​1,409.7 
A) 705.9 
B) ​703.9 
C) ​706.9 
D) ​704.9 
E) ​1,409.7

Question 10

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

Accepted Answer

A) ​​||v|| =   ; θ = 269° 
B) ​​||v|| =   ; θ = 239° 
C) ​​||v|| =   ; θ = 260° 
D) ​||v|| =   ; θ = 252° 
E) ​​||v|| =   ; θ = 279° 
A) ​​||v|| =   ; θ = 269° 
B) ​​||v|| =   ; θ = 239° 
C) ​​||v|| =   ; θ = 260° 
D) ​||v|| =   ; θ = 252° 
E) ​​||v|| =   ; θ = 279°

Question 11

Find the area of the triangle having the indicated angle and sides. ​
B = 123°, a = 64, c = 28
​
(Round your answer to one decimal place.)
​

Accepted Answer

A) 750.4 
B) 753.4 
C) 1,502.9 
D) 752.4 
E) 751.4 
A) 750.4 
B) 753.4 
C) 1,502.9 
D) 752.4 
E) 751.4

Question 12

Find u + v. ​   ​

Accepted Answer

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

Question 13

A straight road makes an angle, A, of 11   with the horizontal.When the angle of elevation, B, of the sun is 52   , a vertical pole beside the road casts a shadow 6 feet long parallel to the road, see figure.Approximate the length of the pole.Round answer to two decimal places.

Accepted Answer

A) 1.86 feet 
B) 5.63 feet 
C) 6.39 feet 
D) 7.68 feet 
E) 5.00 feet 
A) 1.86 feet 
B) 5.63 feet 
C) 6.39 feet 
D) 7.68 feet 
E) 5.00 feet

Question 14

Three forces with magnitudes of 74 pounds, 98 pounds, and 105 pounds act on an object at angles 170°, 220°, and 330°, respectively, with the positive x-axis.Find the magnitude and direction of the resultant force.Round answers to two decimal places.

Accepted Answer

A) 99.08 pounds; 240.95° 
B) 99.08 pounds; 60.95° 
C) 117.42 pounds; 240.95° 
D) 139.13 pounds; 272.47° 
E) 117.42 pounds; 60.95° 
A) 99.08 pounds; 240.95° 
B) 99.08 pounds; 60.95° 
C) 117.42 pounds; 240.95° 
D) 139.13 pounds; 272.47° 
E) 117.42 pounds; 60.95°

Question 15

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

Accepted Answer

A) 510 N-m 
B) 480 N-m 
C) 520 N-m 
D) 500 N-m 
E) 490 N-m 
A) 510 N-m 
B) 480 N-m 
C) 520 N-m 
D) 500 N-m 
E) 490 N-m

Question 16

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64   31   , a = 10 ​and c = 8.

Accepted Answer

A) 43.33 sq.units 
B) 32.50 sq.units 
C) 28.89 sq.units 
D) 36.11 sq.units 
E) 39.72 sq.units 
A) 43.33 sq.units 
B) 32.50 sq.units 
C) 28.89 sq.units 
D) 36.11 sq.units 
E) 39.72 sq.units

Question 17

Find values for b such that the triangle has no solutions. ​
A = 24°, a = 13
​

Accepted Answer

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

Question 18

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.
​

Accepted Answer

A) 2,761.4 lb 
B) 2,764.4 lb 
C) 2,763.4 lb 
D) 2,765.4 lb 
E) 2,762.4 lb 
A) 2,761.4 lb 
B) 2,764.4 lb 
C) 2,763.4 lb 
D) 2,765.4 lb 
E) 2,762.4 lb

Question 19

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. ​

Accepted Answer

A) 80.44° 
B) 91.02° 
C) 58.98° 
D) 29.99° 
E) 60.33° 
A) 80.44° 
B) 91.02° 
C) 58.98° 
D) 29.99° 
E) 60.33°

Question 20

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

Accepted Answer

A) 15.73 
B) 12.07 
C) 10.00 
D) 17.32 
E) 14.14 
A) 15.73 
B) 12.07 
C) 10.00 
D) 17.32 
E) 14.14

If and , find .

Select a value for b such that a triangle with A = 33° and a = 4 has no solution.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. C = 40°, a = , b =

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

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form.

Use the dot product to find the magnitude of u if

To approximate the length of a marsh, a surveyor walks 255 meters from point A to point B, then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh. Where a = 225 m, b = 255 m

Find the component form of vector v.

Find the area of the triangle having the indicated angle and sides. B = 71°20', a = 62, c = 24 (Round your answer to one decimal place.)

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

Find the area of the triangle having the indicated angle and sides. B = 123°, a = 64, c = 28 (Round your answer to one decimal place.)

Find u + v.

A straight road makes an angle, A, of 11 with the horizontal.When the angle of elevation, B, of the sun is 52 , a vertical pole beside the road casts a shadow 6 feet long parallel to the road, see figure.Approximate the length of the pole.Round answer to two decimal places.

Three forces with magnitudes of 74 pounds, 98 pounds, and 105 pounds act on an object at angles 170°, 220°, and 330°, respectively, with the positive x-axis.Find the magnitude and direction of the resultant force.Round answers to two decimal places.

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64 31 , a = 10 and c = 8.

Find values for b such that the triangle has no solutions. A = 24°, a = 13

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places.

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

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

​If and , find .

Select a value for b such that a triangle with A = 33° and a = 4 has no solution.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ C = 40°, a = , b = ​

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

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form. ​

Use the dot product to find the magnitude of u if

To approximate the length of a marsh, a surveyor walks 255 meters from point A to point B, then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh. ​ ​ Where a = 225 m, b = 255 m ​

Find the component form of vector v. ​ ​ ​

Find the area of the triangle having the indicated angle and sides. ​ B = 71°20', a = 62, c = 24 ​ (Round your answer to one decimal place.) ​

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

Find the area of the triangle having the indicated angle and sides. ​ B = 123°, a = 64, c = 28 ​ (Round your answer to one decimal place.) ​

Find u + v. ​ ​

A straight road makes an angle, A, of 11 with the horizontal.When the angle of elevation, B, of the sun is 52 , a vertical pole beside the road casts a shadow 6 feet long parallel to the road, see figure.Approximate the length of the pole.Round answer to two decimal places.

Three forces with magnitudes of 74 pounds, 98 pounds, and 105 pounds act on an object at angles 170°, 220°, and 330°, respectively, with the positive x-axis.Find the magnitude and direction of the resultant force.Round answers to two decimal places.

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64 31 , a = 10 ​and c = 8.

Find values for b such that the triangle has no solutions. ​ A = 24°, a = 13 ​

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place. ​

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. ​

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

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

If and , find .

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. C = 40°, a = , b =

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form.

To approximate the length of a marsh, a surveyor walks 255 meters from point A to point B, then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh. Where a = 225 m, b = 255 m

Find the component form of vector v.

Find the area of the triangle having the indicated angle and sides. B = 71°20', a = 62, c = 24 (Round your answer to one decimal place.)

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

Find the area of the triangle having the indicated angle and sides. B = 123°, a = 64, c = 28 (Round your answer to one decimal place.)

Find u + v.

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64 31 , a = 10 and c = 8.

Find values for b such that the triangle has no solutions. A = 24°, a = 13

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places.