Trigonometry (MindTap Course List)
10th Edition
ISBN: 9781337278461
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 3.3, Problem 107E
(a)
To determine
The geometric description of
(b)
To determine
The geometric description of scalar multiplication.
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Chapter 3 Solutions
Trigonometry (MindTap Course List)
Ch. 3.1 - For the triangle shown, A=30, B=45, and a=32...Ch. 3.1 - Find the height of the tree shown in the figure.Ch. 3.1 - Given A=31,a=12 inches, and b=5 inches, find the...Ch. 3.1 - Show that there is no triangle for which a=4 feet,...Ch. 3.1 - Prob. 5ECPCh. 3.1 - Find the area of a triangular lot with two sides...Ch. 3.1 - On a small lake, you swim from point A to point B...Ch. 3.1 - Prob. 1ECh. 3.1 - For triangle ABC, the Law of Sines is...Ch. 3.1 - Prob. 3E
Ch. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Using the Law of Sines In Exercises 5-22, use the...Ch. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Using the Law of Sines In Exercises 23-32, use the...Ch. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Using the Law of Sines In Exercises 23–32, use the...Ch. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Finding the Area of a Triangle In Exercises 37-44,...Ch. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Height A tree grows at an angle of 4 from the...Ch. 3.1 - A boat is traveling due east parallel to the...Ch. 3.1 - Environmental Science The bearing from the Pine...Ch. 3.1 - Bridge Design A bridge is built across a small...Ch. 3.1 - Angle of Elevation A 10 -meter utility pole casts...Ch. 3.1 - Flight Path A plane flies 500 kilometers with ab...Ch. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Distance Air traffic controllers continuously...Ch. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - True or False? In Exercises 55-58, determine...Ch. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.2 - Find the three angles of the triangle whose sides...Ch. 3.2 - Given A=80,b=16 meters, and c=12 meters, find the...Ch. 3.2 - In a softball game, a batter hits a ball to dead...Ch. 3.2 - Prob. 4ECPCh. 3.2 - Prob. 5ECPCh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Solving a Triangle In Exercises 31-36, determine...Ch. 3.2 - Prob. 37ECh. 3.2 - Using Heron’s Area Formula In Exercises 37-44, use...Ch. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Surveying To approximate the length of a marsh, a...Ch. 3.2 - Streetlight design Determine the angle in the...Ch. 3.2 - Baseball A baseball player in center field is...Ch. 3.2 - Baseball On a baseball diamond with 90-foot sides,...Ch. 3.2 - Prob. 49ECh. 3.2 - Navigation On a map, Minneapolis is 165...Ch. 3.2 - Navigation A boat race runs along a triangular...Ch. 3.2 - Air Navigation A plane flies 810 miles from...Ch. 3.2 - Surveying A triangular parcel of land has 115...Ch. 3.2 - Prob. 54ECh. 3.2 - Distance Two ships leave a port at 9.M.. One...Ch. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - True or False? In Exercises 61 and 62, determine...Ch. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - HOW DO YOU SEE IT? To solve the triangle, would...Ch. 3.2 - Prob. 67ECh. 3.3 - Show that u and v in the figure at the right are...Ch. 3.3 - Prob. 2ECPCh. 3.3 - Prob. 3ECPCh. 3.3 - Prob. 4ECPCh. 3.3 - Prob. 5ECPCh. 3.3 - Prob. 6ECPCh. 3.3 - Prob. 7ECPCh. 3.3 - Prob. 8ECPCh. 3.3 - Prob. 9ECPCh. 3.3 - Prob. 10ECPCh. 3.3 - Prob. 11ECPCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Prob. 41ECh. 3.3 - Finding a Unit Vector In Exercises 4146, find a...Ch. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Prob. 44ECh. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Writing a Linear Combination of Unit Vectors In...Ch. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.3 - Prob. 64ECh. 3.3 - Prob. 65ECh. 3.3 - Prob. 66ECh. 3.3 - Prob. 67ECh. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Using the Law of Cosines In Exercises 73 and 74,...Ch. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 3.3 - Prob. 77ECh. 3.3 - Velocity Pitcher Aroldis Chapman threw a pitch...Ch. 3.3 - Prob. 79ECh. 3.3 - Prob. 80ECh. 3.3 - Prob. 81ECh. 3.3 - Prob. 82ECh. 3.3 - Cable Tension The cranes shown in the figure are...Ch. 3.3 - Prob. 84ECh. 3.3 - Prob. 85ECh. 3.3 - Physics Use the figure to determine the tension...Ch. 3.3 - Prob. 87ECh. 3.3 - Prob. 88ECh. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Air Navigation An airplane travels in the...Ch. 3.3 - Prob. 94ECh. 3.3 - Prob. 95ECh. 3.3 - True or False? In Exercises 9598, determine...Ch. 3.3 - True or False? In Exercises 9598, determine...Ch. 3.3 - Prob. 98ECh. 3.3 - Error Analysis Describe the error in finding the...Ch. 3.3 - Prob. 100ECh. 3.3 - Prob. 101ECh. 3.3 - Technology Write a program for your graphing...Ch. 3.3 - Finding the Difference of Two Vectors In Exercises...Ch. 3.3 - Finding the Difference of Two Vectors In Exercises...Ch. 3.3 - Graphical Reasoning Consider two forces...Ch. 3.3 - Prob. 106ECh. 3.3 - Prob. 107ECh. 3.3 - Prob. 108ECh. 3.4 - Find each dot product. a. 3,42,3 b. 3,51,8 c....Ch. 3.4 - Prob. 2ECPCh. 3.4 - Find the angle between u=2,1 and v=1,3.Ch. 3.4 - Prob. 4ECPCh. 3.4 - Prob. 5ECPCh. 3.4 - Prob. 6ECPCh. 3.4 - Prob. 7ECPCh. 3.4 - Prob. 1ECh. 3.4 - Vocabulary: Fill in the blanks. The dot product of...Ch. 3.4 - Prob. 3ECh. 3.4 - Fill in the blanks. The vectors u and v are if...Ch. 3.4 - Fill in the blanks. The projection of u onto v is...Ch. 3.4 - Fill in the blanks. The work W done by a constant...Ch. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Using the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Decomposing a Vector into Components In Exercises...Ch. 3.4 - Decomposing a Vector into Components In Exercises...Ch. 3.4 - Prob. 59ECh. 3.4 - Prob. 60ECh. 3.4 - Finding the Projection of u onto v In Exercises...Ch. 3.4 - Prob. 62ECh. 3.4 - Prob. 63ECh. 3.4 - Prob. 64ECh. 3.4 - Prob. 65ECh. 3.4 - Prob. 66ECh. 3.4 - Prob. 67ECh. 3.4 - Prob. 68ECh. 3.4 - Prob. 69ECh. 3.4 - Prob. 70ECh. 3.4 - Business The vector u=1225,2445 gives the numbers...Ch. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.4 - Prob. 75ECh. 3.4 - Work Determine the work done by a crane lifting a...Ch. 3.4 - Prob. 77ECh. 3.4 - Prob. 78ECh. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.4 - Prob. 81ECh. 3.4 - Prob. 82ECh. 3.4 - Prob. 83ECh. 3.4 - True or False? In Exercises 83 and 84, determine...Ch. 3.4 - Prob. 85ECh. 3.4 - Prob. 86ECh. 3.4 - Prob. 87ECh. 3.4 - Prob. 88ECh. 3.4 - Prob. 89ECh. 3.4 - Prob. 90ECh. 3.4 - Prob. 91ECh. 3.4 - Prob. 92ECh. 3.4 - Prob. 93ECh. 3 - Prob. 1RECh. 3 - Using the Law of Sines In Exercises 112, use the...Ch. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - River Width A surveyor finds that a pier on the...Ch. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Geometry The lengths of the sides of a...Ch. 3 - Prob. 38RECh. 3 - Surveying To approximate the length of a marsh, a...Ch. 3 - Air Navigation Two planes leave an airport at...Ch. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - Prob. 57RECh. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Prob. 75RECh. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Prob. 81RECh. 3 - Prob. 82RECh. 3 - Prob. 83RECh. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Prob. 93RECh. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 97RECh. 3 - Prob. 98RECh. 3 - Prob. 99RECh. 3 - Prob. 100RECh. 3 - Prob. 101RECh. 3 - Prob. 102RECh. 3 - Work Determine the work done by a crane lifting an...Ch. 3 - Prob. 104RECh. 3 - Prob. 105RECh. 3 - Prob. 106RECh. 3 - Prob. 107RECh. 3 - Prob. 108RECh. 3 - Prob. 109RECh. 3 - Prob. 110RECh. 3 - Prob. 111RECh. 3 - Prob. 112RECh. 3 - Prob. 113RECh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Prob. 10TCh. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - Prob. 15TCh. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Determine whether the vectors u=6,10 and v=5,3 are...Ch. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 22TCh. 3 - Take this test as you would take a test in class....Ch. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 17CTCh. 3 - Prob. 18CTCh. 3 - Prob. 19CTCh. 3 - Prob. 20CTCh. 3 - Prob. 21CTCh. 3 - Prob. 22CTCh. 3 - Prob. 23CTCh. 3 - Prob. 24CTCh. 3 - Prob. 25CTCh. 3 - Prob. 26CTCh. 3 - Prob. 27CTCh. 3 - Prob. 28CTCh. 3 - Prob. 29CTCh. 3 - Prob. 30CTCh. 3 - Prob. 31CTCh. 3 - Prob. 32CTCh. 3 - Prob. 33CTCh. 3 - Find a unit vector u in the direction of v=i+jCh. 3 - Prob. 35CTCh. 3 - Prob. 36CTCh. 3 - Prob. 37CTCh. 3 - Prob. 38CTCh. 3 - From a point 200 feet from a flagpole, the angles...Ch. 3 - To determine the angle of elevation of a star in...Ch. 3 - Prob. 41CTCh. 3 - Prob. 42CTCh. 3 - Prob. 43CTCh. 3 - Distance In the figure, a beam of light is...Ch. 3 - Prob. 2PSCh. 3 - Locating Lost Hikers A group of hikers is lost in...Ch. 3 - Prob. 4PSCh. 3 - Prob. 5PSCh. 3 - Prob. 6PSCh. 3 - Prob. 7PSCh. 3 - Prob. 8PSCh. 3 - Prob. 9PSCh. 3 - Prob. 10PSCh. 3 - Prob. 13PSCh. 3 - Prob. 14PS
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