Question 1

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​
A = 130°, a = 40, b = 25
​

Accepted Answer

A) B ≈ 11°, C ≈ 39°, c ≈ 20.05 
B) B ≈ 39°, C ≈ 11°, c ≈ 20.05 
C) B ≈ 28.61°, C ≈ 21.39°, c ≈ 19.05 
D) B ≈ 21.39°, C ≈ 28.61°, c ≈ 19.05 
E) No Solution 
A) B ≈ 11°, C ≈ 39°, c ≈ 20.05 
B) B ≈ 39°, C ≈ 11°, c ≈ 20.05 
C) B ≈ 28.61°, C ≈ 21.39°, c ≈ 19.05 
D) B ≈ 21.39°, C ≈ 28.61°, c ≈ 19.05 
E) No Solution

Question 2

Use the dot product to find the magnitude of u. ​   ​

Accepted Answer

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

Question 3

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point
Terminal Point
(-9, 7)
​(0, 2)
​

Accepted Answer

A) -9i - 5j 
B) ​-5i + 9j 
C) ​​-5i ​- 9j 
D) ​9i - 5j 
E) ​9i + 5j 
A) -9i - 5j 
B) ​-5i + 9j 
C) ​​-5i ​- 9j 
D) ​9i - 5j 
E) ​9i + 5j

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​
A = 33, b = 36, c = 25
​

Accepted Answer

A) 58.21 
B) 353.71 
C) 450.18 
D) 564.33 
E) 399.04 
A) 58.21 
B) 353.71 
C) 450.18 
D) 564.33 
E) 399.04

Question 7

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 140°, b = 8, c = 9
​

Accepted Answer

A) a ≈ 15.98, B ≈ 21.23°, C ≈ 18.77° 
B) a ≈ 8, B ≈ 18.77°, C ≈ 21.23° 
C) a ≈ 15.98, B ≈ 18.77°, C ≈ 21.23° 
D) a ≈ 15.98, B ≈ 20°, C ≈ 20° 
E) a ≈ 9, B ≈ 18.77°, C ≈ 21.23° 
A) a ≈ 15.98, B ≈ 21.23°, C ≈ 18.77° 
B) a ≈ 8, B ≈ 18.77°, C ≈ 21.23° 
C) a ≈ 15.98, B ≈ 18.77°, C ≈ 21.23° 
D) a ≈ 15.98, B ≈ 20°, C ≈ 20° 
E) a ≈ 9, B ≈ 18.77°, C ≈ 21.23°

Question 8

Find values for b such that the triangle has no solutions. ​
A = 54°, a = 19
​

Accepted Answer

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

Question 9

Given   and   , find

Accepted Answer

A) 7 
B) -5 
C) -17 
D) 11 
E) -19 
A) 7 
B) -5 
C) -17 
D) 11 
E) -19

Question 10

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 31 feet horizontally.How much work has been accomplished? Round your answer to one decimal place.

Accepted Answer

A) 1,301.6 foot-pounds 
B) 1,395.0 foot-pounds 
C) 1,610.8 foot-pounds 
D) 1,208.1 foot-pounds 
E) 1,456.2 foot-pounds 
A) 1,301.6 foot-pounds 
B) 1,395.0 foot-pounds 
C) 1,610.8 foot-pounds 
D) 1,208.1 foot-pounds 
E) 1,456.2 foot-pounds

Question 11

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel. ​

Accepted Answer

A) 180,710.4 ft2 
B) 139,977.7 ft2 
C) 94,372.9 ft2 
D) 207,620.4 ft2 
E) 108,426.2 ft2 
A) 180,710.4 ft2 
B) 139,977.7 ft2 
C) 94,372.9 ft2 
D) 207,620.4 ft2 
E) 108,426.2 ft2

Question 12

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 170, B = 20°, C = 15°
​

Accepted Answer

A) Law of Cosines; No solution 
B) Law of Sines; A = 145°, b ≈ 76.71, c ≈ 101.37 
C) Law of Sines; A = 145°, b ≈ 101.37, c ≈ 76.71 
D) Law of Cosines; A = 145°, b ≈ 101.37, c ≈ 76.71 
E) Law of Sines; No solution 
A) Law of Cosines; No solution 
B) Law of Sines; A = 145°, b ≈ 76.71, c ≈ 101.37 
C) Law of Sines; A = 145°, b ≈ 101.37, c ≈ 76.71 
D) Law of Cosines; A = 145°, b ≈ 101.37, c ≈ 76.71 
E) Law of Sines; No solution

Question 13

Find the projection of u onto v.Then write u as the sum of two orthogonal vectors, one of which is   .​ ​
​     ​

Accepted Answer

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

Question 14

A park ranger at point A observes a fire in the direction N25°26'E.Another ranger at point B, 4 miles due east of A, sites the same fire at N58°34'W.Determine the distance from point B to the fire.Round answer to two decimal places.

Accepted Answer

A) 1.73 miles 
B) 3.63 miles 
C) 2.05 miles 
D) 4.08 miles 
E) 3.43 miles 
A) 1.73 miles 
B) 3.63 miles 
C) 2.05 miles 
D) 4.08 miles 
E) 3.43 miles

Question 15

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 46°, B = 39°, c = 1.4
​

Accepted Answer

A) Law of Cosines; No solution 
B) Law of Sines; No solution 
C) Law of Cosines; C = 95°, a ≈ 0.88, b ≈ 1.01 
D) Law of Sines; C = 95°, a ≈ 1.01, b ≈ 0.88 
E) Law of Sines; C = 95°, a ≈ 1.01, b ≈ 1.01 
A) Law of Cosines; No solution 
B) Law of Sines; No solution 
C) Law of Cosines; C = 95°, a ≈ 0.88, b ≈ 1.01 
D) Law of Sines; C = 95°, a ≈ 1.01, b ≈ 0.88 
E) Law of Sines; C = 95°, a ≈ 1.01, b ≈ 1.01

Question 16

Given a = 9, b = 13, and c = 8, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places.   Figure not drawn to scale

Accepted Answer

A) 99.59° 
B) 80.44° 
C) 37.36° 
D) 43.05° 
E) 60.33° 
A) 99.59° 
B) 80.44° 
C) 37.36° 
D) 43.05° 
E) 60.33°

Question 17

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. ​
A = 13.22, b = 9.36, c = 15.95
​

Accepted Answer

A) 35.77 
B) ​14.09 
C) ​79.16 
D) ​61.84 
E) ​48.31 
A) 35.77 
B) ​14.09 
C) ​79.16 
D) ​61.84 
E) ​48.31

Question 18

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 1.62, b = 0.95, c = 1.45
​

Accepted Answer

A) A ≈ 35.51°, B ≈ 82.06°, C ≈ 62.43° 
B) A ≈ 62.43°, B ≈ 35.51°, C ≈ 82.06° 
C) A ≈ 82.06°, B ≈ 35.51°, C ≈ 62.43° 
D) A ≈ 82.06°, B ≈ 62.43°, C ≈ 35.51° 
E) A ≈ 62.43°, B ≈ 82.06°, C ≈ 35.51° 
A) A ≈ 35.51°, B ≈ 82.06°, C ≈ 62.43° 
B) A ≈ 62.43°, B ≈ 35.51°, C ≈ 82.06° 
C) A ≈ 82.06°, B ≈ 35.51°, C ≈ 62.43° 
D) A ≈ 82.06°, B ≈ 62.43°, C ≈ 35.51° 
E) A ≈ 62.43°, B ≈ 82.06°, C ≈ 35.51°

Question 19

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​
C = 64.47°, a = 39, c = 50
​

Accepted Answer

A) A ≈ 70.79°, B ≈ 44.74°, b ≈ 52.32 
B) A ≈ 70.53°, B ≈ 45°, b ≈ 50 
C) A ≈ 44.74°, B ≈ 70.79°, b ≈ 52.32 
D) A ≈ 45°, B ≈ 70.53°, b ≈ 50 
E) No Solution 
A) A ≈ 70.79°, B ≈ 44.74°, b ≈ 52.32 
B) A ≈ 70.53°, B ≈ 45°, b ≈ 50 
C) A ≈ 44.74°, B ≈ 70.79°, b ≈ 52.32 
D) A ≈ 45°, B ≈ 70.53°, b ≈ 50 
E) No Solution

Question 20

Find values for b such that the triangle has two solutions. ​
A = 10°, a = 18.6
​

Accepted Answer

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

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 130°, a = 40, b = 25

Use the dot product to find the magnitude of u.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 7) (0, 2)

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

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

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 33, b = 36, c = 25

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 140°, b = 8, c = 9

Find values for b such that the triangle has no solutions. A = 54°, a = 19

Given and , find

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 31 feet horizontally.How much work has been accomplished? Round your answer to one decimal place.

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel.

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 170, B = 20°, C = 15°

Find the projection of u onto v.Then write u as the sum of two orthogonal vectors, one of which is .

A park ranger at point A observes a fire in the direction N25°26'E.Another ranger at point B, 4 miles due east of A, sites the same fire at N58°34'W.Determine the distance from point B to the fire.Round answer to two decimal places.

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 46°, B = 39°, c = 1.4

Given a = 9, b = 13, and c = 8, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. Figure not drawn to scale

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. A = 13.22, b = 9.36, c = 15.95

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 1.62, b = 0.95, c = 1.45

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. C = 64.47°, a = 39, c = 50

Find values for b such that the triangle has two solutions. A = 10°, a = 18.6

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​ A = 130°, a = 40, b = 25 ​

Use the dot product to find the magnitude of u. ​ ​

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 7) ​(0, 2) ​

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

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

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​ A = 33, b = 36, c = 25 ​

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 140°, b = 8, c = 9 ​

Find values for b such that the triangle has no solutions. ​ A = 54°, a = 19 ​

Given and , find

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 31 feet horizontally.How much work has been accomplished? Round your answer to one decimal place.

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel. ​

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​ A = 170, B = 20°, C = 15° ​

Find the projection of u onto v.Then write u as the sum of two orthogonal vectors, one of which is .​ ​ ​ ​

A park ranger at point A observes a fire in the direction N25°26'E.Another ranger at point B, 4 miles due east of A, sites the same fire at N58°34'W.Determine the distance from point B to the fire.Round answer to two decimal places.

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​ A = 46°, B = 39°, c = 1.4 ​

Given a = 9, b = 13, and c = 8, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. Figure not drawn to scale

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. ​ A = 13.22, b = 9.36, c = 15.95 ​

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 1.62, b = 0.95, c = 1.45 ​

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​ C = 64.47°, a = 39, c = 50 ​

Find values for b such that the triangle has two solutions. ​ A = 10°, a = 18.6 ​

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 130°, a = 40, b = 25

Use the dot product to find the magnitude of u.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 7) (0, 2)

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

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 33, b = 36, c = 25

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 140°, b = 8, c = 9

Find values for b such that the triangle has no solutions. A = 54°, a = 19

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel.

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 170, B = 20°, C = 15°

Find the projection of u onto v.Then write u as the sum of two orthogonal vectors, one of which is .

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 46°, B = 39°, c = 1.4

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. A = 13.22, b = 9.36, c = 15.95

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 1.62, b = 0.95, c = 1.45

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. C = 64.47°, a = 39, c = 50

Find values for b such that the triangle has two solutions. A = 10°, a = 18.6