Question 1

Find the angle   between the vectors. ​   ​
(Round the answer to 1 decimal place.)
​

Accepted Answer

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

Question 2

A straight road makes an angle, A, of 10° with the horizontal.When the angle of elevation, B, of the sun is 56°, a vertical pole beside the road casts a shadow 8 feet long parallel to the road, see figure.Approximate the length of the pole.Round answer to two decimal places.

Accepted Answer

A) 2.48 feet 
B) 10.29 feet 
C) 6.22 feet 
D) 11.86 feet 
E) 6.94 feet 
A) 2.48 feet 
B) 10.29 feet 
C) 6.22 feet 
D) 11.86 feet 
E) 6.94 feet

Question 3

Find the dot product of u and v. ​   ​

Accepted Answer

A) -10 
B) -8 
C) -4 
D) -6 
E) -2 
A) -10 
B) -8 
C) -4 
D) -6 
E) -2

Question 4

Find the component form of v if   and the angle it makes with the x-axis is 120°.

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Find the dot product of u and v. ​   ​

Accepted Answer

A) 36 
B) 40 
C) 44 
D) 42 
E) 38 
A) 36 
B) 40 
C) 44 
D) 42 
E) 38

Question 8

Given vectors   and   determine the quantity indicated below.

Accepted Answer

A) -48 
B) -56 
C) -46 
D) 88 
E) 20 
A) -48 
B) -56 
C) -46 
D) 88 
E) 20

Question 9

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle A between them (see figure).Determine the distance a between the planes when A = 44°, b = 37 miles, and c = 22 miles. ​   ​

Accepted Answer

A) 35.60 miles 
B) 31.81 miles 
C) 26.11 miles 
D) 11.27 miles 
E) 54.99 miles 
A) 35.60 miles 
B) 31.81 miles 
C) 26.11 miles 
D) 11.27 miles 
E) 54.99 miles

Question 10

Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree, the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree. ​   ​c = 43 m
B = 96°
​
(Round your answer to two decimal places.)
​

Accepted Answer

A) 24.58 m 
B) 26.58 m 
C) 25.58 m 
D) 28.58 m 
E) 27.58 m 
A) 24.58 m 
B) 26.58 m 
C) 25.58 m 
D) 28.58 m 
E) 27.58 m

Question 11

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​
A = 125°, B = 45°, c = 13
​

Accepted Answer

A) C = 10°, a ≈ 61.33, b ≈ 52.94 
B) C = 10°, a ≈ 54.94, b ≈ 62.33 
C) ​C = 10°, a ≈ 53.94, b ≈ 52.94 
D) ​C = 10°, a ≈ 64.33, b ≈ 52.94 
E) ​C = 10°, a ≈ 63.33, b ≈ 54.94 
A) C = 10°, a ≈ 61.33, b ≈ 52.94 
B) C = 10°, a ≈ 54.94, b ≈ 62.33 
C) ​C = 10°, a ≈ 53.94, b ≈ 52.94 
D) ​C = 10°, a ≈ 64.33, b ≈ 52.94 
E) ​C = 10°, a ≈ 63.33, b ≈ 54.94

Question 12

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ​
A = 38°, a = 8, b = 5
​

Accepted Answer

A) B ≈ 29°, C ≈ 113° 
B) B ≈ 22.63°, C ≈ 119.37° 
C) B ≈ 103°, C ≈ 39° 
D) B ≈ 113°, C ≈ 29° 
E) B ≈ 119.37°, C ≈ 22.63° 
A) B ≈ 29°, C ≈ 113° 
B) B ≈ 22.63°, C ≈ 119.37° 
C) B ≈ 103°, C ≈ 39° 
D) B ≈ 113°, C ≈ 29° 
E) B ≈ 119.37°, C ≈ 22.63°

Question 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 θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.
​

Accepted Answer

A) 19.4° 
B) ​21.4° 
C) ​23.4° 
D) ​20.4° 
E) ​22.4° 
A) 19.4° 
B) ​21.4° 
C) ​23.4° 
D) ​20.4° 
E) ​22.4°

Question 14

Find u - v. ​   ​

Accepted Answer

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

Question 15

Find the area of the triangle having the indicated angle and sides. ​   ​
(Round your answer to one decimal place.)
​

Accepted Answer

A) ​4.9 
B) 5.9 
C) 7.9 
D) 6.9 
E) 11.7 
A) ​4.9 
B) 5.9 
C) 7.9 
D) 6.9 
E) 11.7

Question 16

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

Accepted Answer

A) 40 
B)    
C)    
D)    
E) 35 
A) 40 
B)    
C)    
D)    
E) 35

Question 17

Use the Law of Sines to solve for C and B.Round your answer to two decimal places. ​
A = 60°, a = 36, c = 40
​

Accepted Answer

A) C ≈ 105.79°, B ≈ 45.79° or
​C ≈ 74.21°, B ≈ 14.21° 
B) ​C ≈ 74.21°, B ≈ 45.79° or
​C ≈ 105.79°, B ≈ 14.21° 
C) ​C ≈ 10°, B ≈ 110° or
​C ≈ 25.5°, B ≈ 104.5° 
D) ​C ≈ 45.79°, B ≈ 74.21° or
​C ≈ 14.21°, B ≈ 105.79° 
E) ​C ≈ 60°, B ≈ 60° or
​C ≈ 45°, B ≈ 75° 
A) C ≈ 105.79°, B ≈ 45.79° or
​C ≈ 74.21°, B ≈ 14.21° 
B) ​C ≈ 74.21°, B ≈ 45.79° or
​C ≈ 105.79°, B ≈ 14.21° 
C) ​C ≈ 10°, B ≈ 110° or
​C ≈ 25.5°, B ≈ 104.5° 
D) ​C ≈ 45.79°, B ≈ 74.21° or
​C ≈ 14.21°, B ≈ 105.79° 
E) ​C ≈ 60°, B ≈ 60° or
​C ≈ 45°, B ≈ 75°

Question 18

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 55°43', a = 6.5, and b = 14

Accepted Answer

A) 30.08 sq.units 
B) 45.11 sq.units 
C) 33.84 sq.units 
D) 41.35 sq.units 
E) 37.59 sq.units 
A) 30.08 sq.units 
B) 45.11 sq.units 
C) 33.84 sq.units 
D) 41.35 sq.units 
E) 37.59 sq.units

Question 19

​Find the vector v that has a magnitude of 9 and is in the same direction as u, where   . ​

Accepted Answer

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

Question 20

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 84°38', a = 7, and c = 8

Accepted Answer

A) 33.45 sq.units 
B) 27.88 sq.units 
C) 25.09 sq.units 
D) 30.66 sq.units 
E) 22.30 sq.units 
A) 33.45 sq.units 
B) 27.88 sq.units 
C) 25.09 sq.units 
D) 30.66 sq.units 
E) 22.30 sq.units

Find the angle between the vectors. (Round the answer to 1 decimal place.)

A straight road makes an angle, A, of 10° with the horizontal.When the angle of elevation, B, of the sun is 56°, a vertical pole beside the road casts a shadow 8 feet long parallel to the road, see figure.Approximate the length of the pole.Round answer to two decimal places.

Find the dot product of u and v.

Find the component form of v if and the angle it makes with the x-axis is 120°.

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

Use the dot product to find the magnitude of u.

Find the dot product of u and v.

Given vectors and determine the quantity indicated below.

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle A between them (see figure).Determine the distance a between the planes when A = 44°, b = 37 miles, and c = 22 miles.

Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree, the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree. c = 43 m B = 96° (Round your answer to two decimal places.)

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 125°, B = 45°, c = 13

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. A = 38°, a = 8, b = 5

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 θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.

Find u - v.

Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.)

Use the dot product to find the magnitude of u.

Use the Law of Sines to solve for C and B.Round your answer to two decimal places. A = 60°, a = 36, c = 40

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 55°43', a = 6.5, and b = 14

Find the vector v that has a magnitude of 9 and is in the same direction as u, where .

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 84°38', a = 7, and c = 8

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

Find the angle between the vectors. ​ ​ (Round the answer to 1 decimal place.) ​

A straight road makes an angle, A, of 10° with the horizontal.When the angle of elevation, B, of the sun is 56°, a vertical pole beside the road casts a shadow 8 feet long parallel to the road, see figure.Approximate the length of the pole.Round answer to two decimal places.

Find the dot product of u and v. ​ ​

Find the component form of v if and the angle it makes with the x-axis is 120°.

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

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

Find the dot product of u and v. ​ ​

Given vectors and determine the quantity indicated below.

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle A between them (see figure).Determine the distance a between the planes when A = 44°, b = 37 miles, and c = 22 miles. ​ ​

Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree, the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree. ​ ​c = 43 m B = 96° ​ (Round your answer to two decimal places.) ​

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​ A = 125°, B = 45°, c = 13 ​

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ​ A = 38°, a = 8, b = 5 ​

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 θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place. ​

Find u - v. ​ ​

Find the area of the triangle having the indicated angle and sides. ​ ​ (Round your answer to one decimal place.) ​

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

Use the Law of Sines to solve for C and B.Round your answer to two decimal places. ​ A = 60°, a = 36, c = 40 ​

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 55°43', a = 6.5, and b = 14

​Find the vector v that has a magnitude of 9 and is in the same direction as u, where . ​

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 84°38', a = 7, and c = 8

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find the angle between the vectors. (Round the answer to 1 decimal place.)

Find the dot product of u and v.

Use the dot product to find the magnitude of u.

Find the dot product of u and v.

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle A between them (see figure).Determine the distance a between the planes when A = 44°, b = 37 miles, and c = 22 miles.

Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree, the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree. c = 43 m B = 96° (Round your answer to two decimal places.)

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 125°, B = 45°, c = 13

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. A = 38°, a = 8, b = 5

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 θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.

Find u - v.

Find the area of the triangle having the indicated angle and sides. (Round your answer to one decimal place.)

Use the dot product to find the magnitude of u.

Use the Law of Sines to solve for C and B.Round your answer to two decimal places. A = 60°, a = 36, c = 40

Find the vector v that has a magnitude of 9 and is in the same direction as u, where .