Question 1

Given that   , find the number.

Accepted Answer

A) -6 
B) -2 
C) 26 
D) -4 
E) 22 
A) -6 
B) -2 
C) 26 
D) -4 
E) 22

Question 2

The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.

Accepted Answer

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

Question 3

Two tugboats are towing a large ship into port, as shown in the figure. The larger tug exerts a force of 4,100 pounds on its cable, and the smaller tug exerts a force of 3,500 pounds on its cable.   If the ship is to travel on a straight line l, approximate the angle   that the larger tug must make with l.

Accepted Answer

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

Question 4

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 5

Find 4a - 6b. a = i + 4j, b = 5i - 2j

Accepted Answer

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

Question 6

A rhombus has sides of length 115 centimeters, and the angle at one of the vertices is 70   . Approximate the lengths of the diagonals to the nearest tenth of a centimeter.

Accepted Answer

A) 39.9 cm , 39.9 cm 
B) 142.1 cm , 187.6 cm 
C) 131.9 cm , 188.4 cm 
D) 142.1 cm , 188.2 cm 
E) 142.7 cm , 187.6 cm 
A) 39.9 cm , 39.9 cm 
B) 142.1 cm , 187.6 cm 
C) 131.9 cm , 188.4 cm 
D) 142.1 cm , 188.2 cm 
E) 142.7 cm , 187.6 cm

Question 7

A straight road makes an angle of   with the horizontal. When the angle of elevation of the sun is   , a vertical pole at the side of the road casts a shadow   feet long directly down the road, as shown in the figure.   Approximate the length of the pole.

Accepted Answer

A) 121.00 ft 
B) 120.40 ft 
C) 79.77 ft 
D) 121.30 ft 
E) 120.10 ft 
A) 121.00 ft 
B) 120.40 ft 
C) 79.77 ft 
D) 121.30 ft 
E) 120.10 ft

Question 8

Use trigonometric forms to find   and   .

Accepted Answer

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

Question 9

Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle   , as shown in the figure.   If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector   .

Accepted Answer

A) 0 
B) 7.23 
C) 7.17 
D) 7.20 
E) 7.99 
A) 0 
B) 7.23 
C) 7.17 
D) 7.20 
E) 7.99

Question 10

A helicopter hovers at an altitude that is   feet above a mountain peak of altitude 5,184 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is   , and from the mountaintop, the angle of elevation is   .   Approximate the altitude of the taller peak.

Accepted Answer

A) 5,437 ft 
B) 5,439 ft 
C) 5,441 ft 
D) 4,931 ft 
E) 5,443 ft 
A) 5,437 ft 
B) 5,439 ft 
C) 5,441 ft 
D) 4,931 ft 
E) 5,443 ft

Question 11

Solve

Accepted Answer

A)    
B)    
C)    
D)    
E) No triangle exists 
A)    
B)    
C)    
D)    
E) No triangle exists

Question 12

The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is   . The real part of I represents the actual current delivered to an electrical appliance in amps. Approximate this current when   and   , and express the answer in rectangular form to two decimal places.

Accepted Answer

A) 1.55 amps 
B) 1.48 amps 
C) 1.43 amps 
D) 2.95 amps 
E) 1.33 amps 
A) 1.55 amps 
B) 1.48 amps 
C) 1.43 amps 
D) 2.95 amps 
E) 1.33 amps

Question 13

Shown in the figure is a plan for the top of a wing of a jet fighter, where   feet and   feet.   Approximate the area of triangle ABC.

Accepted Answer

A) 453.3 ft 2  
B) 452.9 ft 2  
C) 905.7 ft 2  
D) 453.5 ft 2  
E) 453.1 ft 2  
A) 453.3 ft 2  
B) 452.9 ft 2  
C) 905.7 ft 2  
D) 453.5 ft 2  
E) 453.1 ft 2

Question 14

A rhombus has sides of length 100 centimeters, and the angle at one of the vertices is 70   . Approximate the lengths of the diagonals to the nearest tenth of a centimeter.

Accepted Answer

A) 125.5 cm , 164.6 cm 
B) 114.7 cm , 163.8 cm 
C) 124.9 cm , 164.6 cm 
D) 124.9 cm , 163.6 cm 
E) 34.7 cm , 34.7 cm 
A) 125.5 cm , 164.6 cm 
B) 114.7 cm , 163.8 cm 
C) 124.9 cm , 164.6 cm 
D) 124.9 cm , 163.6 cm 
E) 34.7 cm , 34.7 cm

Question 15

Determine whether the given pair of vectors are orthogonal or not.   and

Accepted Answer

A) no 
B) yes 
A) no 
B) yes

Question 16

Find the four fourth roots of   .

Accepted Answer

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

Question 17

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field (   ).

Accepted Answer

A) 10.89 acres 
B) 11.17 acres 
C) 3.39 acres 
D) 11.50 acres 
E) 10.30 acres 
A) 10.89 acres 
B) 11.17 acres 
C) 3.39 acres 
D) 11.50 acres 
E) 10.30 acres

Question 18

If forces F 1 , F 2 ,..., F n  act at a point P, the net (or resultant) force F is the sum   If   the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.

Accepted Answer

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

Question 19

A jet airplane approaches a runway at an angle of   with the horizontal, traveling at a speed of 175 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Accepted Answer

A) vertical = 25.56 mi/hr, horizontal = 173.30 mi/hr 
B) vertical = 173.30 mi/hr , horizontal = 173.30 mi/hr 
C) vertical = 25.56 mi/hr, horizontal = 25.56 mi/hr 
D) vertical = 24.36 mi/hr, horizontal = 173.30 mi/hr 
E) vertical = 20.76 mi/hr, horizontal = 173.30 mi/hr 
A) vertical = 25.56 mi/hr, horizontal = 173.30 mi/hr 
B) vertical = 173.30 mi/hr , horizontal = 173.30 mi/hr 
C) vertical = 25.56 mi/hr, horizontal = 25.56 mi/hr 
D) vertical = 24.36 mi/hr, horizontal = 173.30 mi/hr 
E) vertical = 20.76 mi/hr, horizontal = 173.30 mi/hr

Question 20

Find 3a + 6b. a = , b =

Accepted Answer

A) 3a + 6b =  
B) 3a + 6b =  
C) 3a + 6b =  
D) 3a + 6b =  
E) 3a + 6b =  
A) 3a + 6b =  
B) 3a + 6b =  
C) 3a + 6b =  
D) 3a + 6b =  
E) 3a + 6b =

Given that , find the number.

The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find 4a - 6b. a = i + 4j, b = 5i - 2j

A rhombus has sides of length 115 centimeters, and the angle at one of the vertices is 70 . Approximate the lengths of the diagonals to the nearest tenth of a centimeter.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

Use trigonometric forms to find and .

Solve

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate the area of triangle ABC.

A rhombus has sides of length 100 centimeters, and the angle at one of the vertices is 70 . Approximate the lengths of the diagonals to the nearest tenth of a centimeter.

Determine whether the given pair of vectors are orthogonal or not. and

Find the four fourth roots of .

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).

If forces F₁, F₂,..., F_n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.

A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 175 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Find 3a + 6b. a = < 5, - 3>, b = <4, 6 >

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

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Exam 8: Applications of Trigonometry

Given that , find the number.

The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find 4a - 6b. a = i + 4j, b = 5i - 2j

A rhombus has sides of length 115 centimeters, and the angle at one of the vertices is 70 . Approximate the lengths of the diagonals to the nearest tenth of a centimeter.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

Use trigonometric forms to find and .

Solve

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate the area of triangle ABC.

A rhombus has sides of length 100 centimeters, and the angle at one of the vertices is 70 . Approximate the lengths of the diagonals to the nearest tenth of a centimeter.

Determine whether the given pair of vectors are orthogonal or not. and

Find the four fourth roots of .

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).

If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.

A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 175 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Find 3a + 6b. a = < 5, - 3>, b = <4, 6 >

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

If forces F₁, F₂,..., F_n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.