Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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Chapter 7.3, Problem 68E
To determine
To calculate: The area of the
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Chapter 7 Solutions
Trigonometry (11th Edition)
Ch. 7.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.1 -
CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.1 -
CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.1 - CONCEPT PREVIEW Consider each case and determine...Ch. 7.1 - CONCEPT PREVIEW Consider each case and determine...Ch. 7.1 - CONCEPT PREVIEW Consider each case and determine...Ch. 7.1 - CONCEPT PREVIEW Consider each case and determine...
Ch. 7.1 - Find the length of each side labeled a. Do not use...Ch. 7.1 - Find the length of each side labeled a. Do not use...Ch. 7.1 -
Determine the remaining sides and angles of each...Ch. 7.1 -
Determine the remaining sides and angles of each...Ch. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 -
Determine the remaining sides and angles of each...Ch. 7.1 -
Determine the remaining sides and angles of each...Ch. 7.1 -
Determine the remaining sides and angles of each...Ch. 7.1 - Prob. 19ECh. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 -
Determine the remaining sides and angles of each...Ch. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 - Determine the remaining side s and angles of each...Ch. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 - Determine the remaining sides and angles of each...Ch. 7.1 - Why can the law of sines not be used to solve a...Ch. 7.1 - 30. In Example 1, we begin (as seen there) by...Ch. 7.1 -
31. Eli Maor, a perceptive trigonometry student,...Ch. 7.1 - Prob. 32ECh. 7.1 -
33. Distance across a River To find the distance...Ch. 7.1 - Distance across a Canyon To determine the distance...Ch. 7.1 - Distance a Ship Travels A ship is sailing due...Ch. 7.1 -
36. Distance between Radio Direction Finders...Ch. 7.1 - Distance between a Ship and a Lighthouse The...Ch. 7.1 -
38. Distance across a River Standing on one bank...Ch. 7.1 - Height of a Balloon A balloonist is directly above...Ch. 7.1 -
40. Measurement of a Folding Chair A folding...Ch. 7.1 -
41. Angle Formed by Radii of Gears Three gears...Ch. 7.1 -
42. Distance between Atoms Three atoms with...Ch. 7.1 -
43. Distance to the Moon The moon is a relatively...Ch. 7.1 - Ground Distances Measured by Aerial Photography...Ch. 7.1 -
45. Ground Distances Measured by Aerial...Ch. 7.1 - 46. Ground Distances Measured by...Ch. 7.1 - Find the area of each triangle using the formula A...Ch. 7.1 - Prob. 48ECh. 7.1 - Find the area of each triangle using the formula A...Ch. 7.1 - Find the area of each triangle using the formula A...Ch. 7.1 - Find the area of each triangle ABC. See Examples 4...Ch. 7.1 -
Find the area of each triangle ABC. See Examples...Ch. 7.1 - Prob. 53ECh. 7.1 -
Find the area of each triangle ABC. See Examples...Ch. 7.1 -
Find the area of each triangle ABC. See Examples...Ch. 7.1 -
Find the area of each triangle ABC. See Examples...Ch. 7.1 -
Find the area of each triangle ABC. See Examples...Ch. 7.1 - Prob. 58ECh. 7.1 - Area of a Metal Plate A painter is going to apply...Ch. 7.1 - Prob. 60ECh. 7.1 - Triangle Inscribed in a Circle For a triangle...Ch. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Aerial Photography Aerial photographs can be used...Ch. 7.2 -
1. CONCEPT PREVIEW Which one of the following...Ch. 7.2 - CONCEPT PREVIEW Which one of the following sets of...Ch. 7.2 - CONCEPT PREVIEW In each figure, a line segment of...Ch. 7.2 - CONCEPT PREVIEW In each figure, a line segment of...Ch. 7.2 - CONCEPT PREVIEW Determine the number of triangles...Ch. 7.2 - CONCEPT PREVIEW Determine the number of triangles...Ch. 7.2 - Prob. 7ECh. 7.2 - CONCEPT PREVIEW Determine the number of triangles...Ch. 7.2 - CONCEPT PREVIEW Determine the number of triangles...Ch. 7.2 - CONCEPT PREVIEW Determine the number of triangles...Ch. 7.2 - Find each angle B. Do not use a calculator.Ch. 7.2 - Find each angle B. Do not use a calculator.Ch. 7.2 - Find the unknown angles in triangle ABC for each...Ch. 7.2 - Find the unknown angles in triangle ABC for each...Ch. 7.2 - Find the unknown angles in triangle ABC for each...Ch. 7.2 - Find the unknown angles in triangle ABC for each...Ch. 7.2 - Find the unknown angles in triangle ABC for each...Ch. 7.2 - Find the unknown angles in triangle ABC for each...Ch. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Solve each triangle ABC that exists. See Examples...Ch. 7.2 - Prob. 22ECh. 7.2 -
Solve each triangle ABC that exists. See Examples...Ch. 7.2 - Prob. 24ECh. 7.2 -
Solve each triangle ABC that exists. See Examples...Ch. 7.2 - Prob. 26ECh. 7.2 -
Solve each triangle ABC that exists. See Examples...Ch. 7.2 -
Solve each triangle ABC that exists. See Examples...Ch. 7.2 -
Solve each triangle ABC that exists. See Examples...Ch. 7.2 -
Solve each triangle ABC that exists. See Examples...Ch. 7.2 - Apply the law of sines to the following:...Ch. 7.2 - Prob. 32ECh. 7.2 - Without using the law of sines, why can no...Ch. 7.2 - Prob. 34ECh. 7.2 - Use the law of sines to solve each problem.
35....Ch. 7.2 - 36. Height of an Antenna Tower The angle of...Ch. 7.2 -
37. Height of a Building A flagpole 95.0 ft tall...Ch. 7.2 -
38. Flight Path of a Plane A pilot flies her...Ch. 7.2 - Use the law of sines to prove that each statement...Ch. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.3 - CONCEPT PREVIEW Assume a triangle ABC has standard...Ch. 7.3 -
CONCEPT PREVIEW Assume a triangle ABC has...Ch. 7.3 - CONCEPT PREVIEW Assume a triangle ABC has standard...Ch. 7.3 -
CONCEPT PREVIEW Assume a triangle ABC has...Ch. 7.3 - CONCEPT PREVIEW Assume a triangle ABC has standard...Ch. 7.3 - CONCEPT PREVIEW Assume a triangle ABC has standard...Ch. 7.3 - CONCEPT PREVIEW Assume a triangle ABC has standard...Ch. 7.3 - Prob. 8ECh. 7.3 - Find the length of the remaining side of each...Ch. 7.3 - Find the length of the remaining side of each...Ch. 7.3 - Find the measure of θ in each triangle. Do not use...Ch. 7.3 - Find the measure of in each triangle. Do not use...Ch. 7.3 - Solve each triangle. Approximate values to the...Ch. 7.3 - Solve each triangle. Approximate values to the...Ch. 7.3 - Solve each triangle. Approximate values to the...Ch. 7.3 - Solve each triangle. Approximate values to the...Ch. 7.3 - Solve each triangle. Approximate values to the...Ch. 7.3 - Prob. 18ECh. 7.3 - Solve each triangle. See Examples 2 and 3. A =...Ch. 7.3 - Solve each triangle. See Examples 2 and 3. C =...Ch. 7.3 - Solve each triangle. See Examples 2 and 3. C =...Ch. 7.3 - Prob. 22ECh. 7.3 -
Solve each triangle. See Examples 2 and 3.
23. a...Ch. 7.3 - Solve each triangle. See Examples 2 and 3. a = 28...Ch. 7.3 - Solve each triangle. See Examples 2 and 3. a =...Ch. 7.3 - Solve each triangle. See Examples 2 and 3. a = 189...Ch. 7.3 - Solve each triangle. See Examples 2 and 3. a = 965...Ch. 7.3 - Prob. 28ECh. 7.3 -
Solve each triangle. See Examples 2 and 3.
29. A...Ch. 7.3 - Prob. 30ECh. 7.3 - Solve each triangle. See Examples 2 and 3. B =...Ch. 7.3 - Prob. 32ECh. 7.3 -
Solve each triangle. See Examples 2 and 3.
33. A...Ch. 7.3 -
Solve each triangle. See Examples 2 and 3.
34. B...Ch. 7.3 -
Solve each triangle. See Examples 2 and 3.
35. a...Ch. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Distance across a River Points A and B arc on...Ch. 7.3 - Prob. 40ECh. 7.3 - Angle in a Parallelogram A parallelogram has sides...Ch. 7.3 -
42. Diagonals of a Parallelogram The sides of a...Ch. 7.3 - 43. Flight Distance Airports A and B are 450 km...Ch. 7.3 -
44. Distance Traveled by a Plane An airplane...Ch. 7.3 - 45. Distance between Ends of the Vietnam Memorial...Ch. 7.3 - Prob. 46ECh. 7.3 - 47. Distance between a Ship and a Rock A ship is...Ch. 7.3 - Distance between a Ship and a Submarine From an...Ch. 7.3 - Truss Construction A triangular truss is shown in...Ch. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - 54. Distance on a Softball Diamond A softball...Ch. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Path of a Ship A ship sailing due east in the...Ch. 7.3 - Length of a Tunnel To measure the distance through...Ch. 7.3 - Prob. 60ECh. 7.3 - Find the measure of each angle θ to two decimal...Ch. 7.3 - Prob. 62ECh. 7.3 - Find the exact area of each triangle using the...Ch. 7.3 - Prob. 64ECh. 7.3 - Find the area of each triangle ABC. See Example...Ch. 7.3 - Prob. 66ECh. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Find the area of each triangle ABC. See Example 5....Ch. 7.3 - Prob. 70ECh. 7.3 - Prob. 71ECh. 7.3 - Prob. 72ECh. 7.3 - Area of the Bermuda Triangle Find the area of the...Ch. 7.3 - Prob. 74ECh. 7.3 - 75. Consider triangle ABC shown here.
(a) Use the...Ch. 7.3 - Prob. 76ECh. 7.3 - Prob. 77ECh. 7.3 - Prob. 78ECh. 7.3 - Prob. 79ECh. 7.3 - Prob. 80ECh. 7.3 - Prob. 1QCh. 7.3 - Prob. 2QCh. 7.3 - Prob. 3QCh. 7.3 - Prob. 4QCh. 7.3 - Find the area of triangle ABC if a = 19.5 km, b =...Ch. 7.3 - Prob. 6QCh. 7.3 - Prob. 7QCh. 7.3 - Height of a Balloon The angles of elevation of a...Ch. 7.3 - Prob. 9QCh. 7.3 - Prob. 10QCh. 7.4 -
Refer to the vectors m through t below.
Name all...Ch. 7.4 - Refer to the vectors m through t below. Name all...Ch. 7.4 - Refer to the vectors m through t below. Name all...Ch. 7.4 - Refer to the vectors m through t below. Name all...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 -
CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 - CONCEPT PREVIEW Refer to vectors a through h...Ch. 7.4 -
17. From the results of Exercises 13 and 14, docs...Ch. 7.4 - From the results of Exercises 15 and 16, docs it...Ch. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Use the parallelogram rule to find the magnitude...Ch. 7.4 - Use the parallelogram rule to find the magnitude...Ch. 7.4 - Use the parallelogram rule to find the magnitude...Ch. 7.4 - Use the parallelogram rule to find the magnitude...Ch. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - 31. Direction and Magnitude of an Equilibrant Two...Ch. 7.4 - Direction and Magnitude of an Equilibrant Two...Ch. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - 35. Magnitudes of Forces A force of 176 lb makes...Ch. 7.4 - Prob. 36ECh. 7.4 -
37. Angle of a Hill Slope A force of 25 lb is...Ch. 7.4 - Prob. 38ECh. 7.4 - 39. Force Needed for a Monolith To build the...Ch. 7.4 - 40. Force Needed for a Monolith If the causeway in...Ch. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Weight of a Crate and Tension of a Rope A crate is...Ch. 7.4 -
45. Distance and Bearing of a Ship A ship leaves...Ch. 7.4 - 46. Distance and Bearing of a Luxury Liner A...Ch. 7.4 - Distance of a Ship from Its Starting Point...Ch. 7.4 -
48. Distance of a Ship from Its Starting Point...Ch. 7.4 - 49. Distance and Direction of a Motorboat A...Ch. 7.4 - Movement of a Motorboat Suppose we would like to...Ch. 7.4 - 51. Hearing and Ground Speed of a Plane An airline...Ch. 7.4 - Path Traveled by a Plane The aircraft carrier...Ch. 7.4 - Airspeed and Ground Speed A pilot wants to fly on...Ch. 7.4 -
54. Bearing of a Plane A plane flies 650 mph on a...Ch. 7.4 -
55. Bearing and Ground Speed of a Plane A pilot...Ch. 7.4 - Bearing and Ground Speed of a Plane A pilot is...Ch. 7.4 - Bearing and Airspeed of a Plane What bearing and...Ch. 7.4 - 58. Ground Speed and Bearing of a Plane A plane is...Ch. 7.4 - Ground Speed and Bearing of a Plane An airplane is...Ch. 7.4 - Prob. 60ECh. 7.5 - CONCEPT PREVIEW Fill in the blank to correctly...Ch. 7.5 - CONCEPT PREVIEW Fill in the blank to correctly...Ch. 7.5 -
CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.5 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 7.5 - Prob. 5ECh. 7.5 - CONCEPT PREVIEW Fill in the blank to correctly...Ch. 7.5 - Prob. 7ECh. 7.5 - CONCEPT PREVIEW Fill in the blank to correctly...Ch. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Find the magnitude and direction angle for each...Ch. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Write each vector in the form (a, b). Round to...Ch. 7.5 - Write each vector in the form (a, b). Round to...Ch. 7.5 - Write each vector in the form (a, b). Round to...Ch. 7.5 - Write each vector in the form (a, b). Round to...Ch. 7.5 - Write each vector in the form (a, b). Round to...Ch. 7.5 - Write each vector in the form (a, b). Round to...Ch. 7.5 - Use the figure to find each vector: (a) u + v (b)...Ch. 7.5 -
Use the figure to find each vector: (a) u + v (b)...Ch. 7.5 - Use the figure to find each vector: (a) u + v (b)...Ch. 7.5 -
Use the figure to find each vector: (a) u + v (b)...Ch. 7.5 - Use the figure to find each vector: (a) u + v (b)...Ch. 7.5 - Use the figure to find each vector: (a) u + v (b)...Ch. 7.5 - Given vectors u and v, find: (a) 2u (b) 2u + 3v...Ch. 7.5 - Given vectors u and v, find: (a) 2u (b) 2u + 3v...Ch. 7.5 - Given vectors u and v, find: (a) 2u (b) 2u + 3v...Ch. 7.5 - Given vectors u and v, find: (a) 2u (b) 2u + 3v...Ch. 7.5 - Given u= 2,5 and v= 4,3 , find each of the...Ch. 7.5 - Given u= 2,5 and v= 4,3 , find each of the...Ch. 7.5 - Given and , find each of the following. See...Ch. 7.5 -
Given and , find each of the following. See...Ch. 7.5 - Given and , find each of the following. See...Ch. 7.5 - Given u= 2,5 and v= 4,3 , find each of the...Ch. 7.5 -
Given and , find each of the following. See...Ch. 7.5 -
Given and , find each of the following. See...Ch. 7.5 -
Write each vector in the form ai + bj.
43.
Ch. 7.5 - Write each vector in the form ai + bj. 6,3Ch. 7.5 - Write each vector in the form ai + bj.
45.
Ch. 7.5 - Write each vector in the form ai + bj. 0,4Ch. 7.5 - Find the dot product for each pair of vectors. See...Ch. 7.5 - Find the dot product for each pair of vectors. See...Ch. 7.5 - Prob. 49ECh. 7.5 - Find the angle between each pair of vectors. See...Ch. 7.5 - Prob. 51ECh. 7.5 - Find the dot product for each pair of vectors. See...Ch. 7.5 - Find the angle between each pair of vectors. See...Ch. 7.5 - Find the angle between each pair of vectors. See...Ch. 7.5 - Prob. 55ECh. 7.5 -
Find the angle between each pair of vectors. See...Ch. 7.5 - Prob. 57ECh. 7.5 - Prob. 58ECh. 7.5 - Let u= 2,1 ,v= 3,4 , and w= 5,12 . Evaluate each...Ch. 7.5 -
Let and . Evaluate each expression.
60. u ·...Ch. 7.5 - Let u= 2,1 ,v= 3,4 , and w= 5,12 . Evaluate each...Ch. 7.5 - Let u= 2,1 ,v= 3,4 , and w= 5,12 . Evaluate each...Ch. 7.5 - Determine whether each pair of vectors is...Ch. 7.5 - Determine whether each pair of vectors is...Ch. 7.5 - Determine whether each pair of vectors is...Ch. 7.5 -
Determine whether each pair of vectors is...Ch. 7.5 - Determine whether each pair of vectors is...Ch. 7.5 - Determine whether each pair of vectors is...Ch. 7.5 - (Modeling) Measuring Rainfall Suppose that vector...Ch. 7.5 - Concept Check In Exercise 69, for the rain gauge...Ch. 7.5 - Consider the two vectors u and v shown. Assume all...Ch. 7.5 - Consider the two vectors u and v shown. Assume all...Ch. 7.5 - Consider the two vectors u and v shown. Assume all...Ch. 7.5 - Prob. 74ECh. 7.5 - Prob. 75ECh. 7.5 - Consider the two vectors u and v shown. Assume all...Ch. 7.5 - Prob. 1SECh. 7.5 - Prob. 2SECh. 7.5 - Distance between Two Lighthouses Two lighthouses...Ch. 7.5 - Prob. 4SECh. 7.5 - Prob. 5SECh. 7.5 - Prob. 6SECh. 7.5 - Wind and Vectors A wind can be described by v = 6i...Ch. 7.5 - 8. Ground Speed and Bearing A plane with an...Ch. 7.5 - Prob. 9SECh. 7.5 - Property Survey A triangular piece of property has...Ch. 7 - Use the law of cosines to find the indicated part...Ch. 7 - Use the law of cosines to find the indicated part...Ch. 7 - Prob. 3RECh. 7 -
Use the law of cosines to find the indicated part...Ch. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 -
Use the law of cosines to find the indicated...Ch. 7 -
Use the law of cosines to find the indicated...Ch. 7 - Use the law of cosines to find the indicated part...Ch. 7 - Use the law of cosines to find the indicated part...Ch. 7 - Use the law of cosines to find the indicated part...Ch. 7 -
Use the law of cosines to find the indicated...Ch. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Find the area of each triangle ABC. a = 0.913 km,...Ch. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Height of a Tree A hill makes an angle of 14.3...Ch. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Given two forces and the angle between them, find...Ch. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - Angle of a Hill A 186-lb force is required to hold...Ch. 7 - Prob. 51RECh. 7 - Prob. 52RECh. 7 - Prob. 53RECh. 7 - Prob. 54RECh. 7 - Law of Tangents In addition to the law of sines...Ch. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Find the indicated part of each triangle ABC. Find...Ch. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - Prob. 10TCh. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Prob. 13TCh. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - Prob. 16TCh. 7 - Prob. 17TCh. 7 - Prob. 18TCh. 7 - Hearing and Airspeed Find the bearing and airspeed...Ch. 7 - Prob. 20T
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