Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Question
Chapter 6.5, Problem 2E
To determine
To choose: The option in which law of sines can be used to solve a triangle.
Expert Solution & Answer
Answer to Problem 2E
The law of sines are be used to solve a triangle by ASA and SSA.
Explanation of Solution
Given information:
The following options are provided,
Formula used:
Law of sines and cosines are used to solve the oblique triangles. Oblique triangles are the triangles with no right triangles.
Law of sines are applicable if the triangles are given with two angles and a side included i.e. ASA or SAA and with two sides and angle opposite one of those sides i.e. SSA.
Law of cosines are applicable when the triangle is given with two sides and included angle i.e. SAS and with all the three sides i.e. SSS.
Calculation:
To find out the options in which law of sines can be used to solve a triangle, recall that law of sines and cosines are used to solve the oblique triangles. Oblique triangles are the triangles with no right triangles.
Law of sines are applicable if the triangles are given with two angles and a side included i.e. ASA or SAA and with two sides and angle opposite one of those sides i.e. SSA.
Law of cosines are applicable when the triangle is given with two sides and included angle i.e. SAS and with all the three sides i.e. SSS.
So, ASA and SSA are the law of sines that are used to solve the triangles.
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
Ch. 6.1 - (a) The radian measure of an angle is the length...Ch. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Prob. 65ECh. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Travel Distance A cars wheels are 28 in. in...Ch. 6.1 - Wheel Revolutions How many revolutions will a car...Ch. 6.1 - Latitudes Pittsburgh, Pennsylvania, and Miami,...Ch. 6.1 - Prob. 72ECh. 6.1 - Prob. 73ECh. 6.1 - Circumference of the Earth The Greek mathematician...Ch. 6.1 - Prob. 75ECh. 6.1 - Irrigation An irrigation system uses a straight...Ch. 6.1 - Windshield Wipers The top and bottom ends of a...Ch. 6.1 - The Tethered Cow A cow is tethered by a 100-ft...Ch. 6.1 - Fan A ceiling fan with 16-in. blades rotates at 45...Ch. 6.1 - Radial Saw A radial saw has a blade with a 6-in....Ch. 6.1 - Winch A winch of radius 2 ft is used to lift heavy...Ch. 6.1 - Speed of a Car The wheels of a car have radius 11...Ch. 6.1 - Speed at the Equator The earth rotates about its...Ch. 6.1 - Truck Wheels A truck with 48-in.-diameter wheels...Ch. 6.1 - Speed of a Current To measure the speed of a...Ch. 6.1 - Bicycle Wheel The sprockets and chain of a bicycle...Ch. 6.1 - Conical Cup A conical cup is made from a circular...Ch. 6.1 - Conical Cup In this exercise we find the volume of...Ch. 6.1 - Prob. 89ECh. 6.1 - Prob. 90ECh. 6.2 - A right triangle with an angle is shown in the...Ch. 6.2 - The reciprocal identities state that...Ch. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Height of a Building The angle of elevation to the...Ch. 6.2 - Gateway Arch A plane is flying within sight of the...Ch. 6.2 - Deviation of a Laser Beam A laser beam is to be...Ch. 6.2 - Distance at Sea From the top of a 200-ft...Ch. 6.2 - Leaning Ladder A 20-ft ladder leans against a...Ch. 6.2 - Prob. 52ECh. 6.2 - Elevation of a Kite A man is lying on the beach,...Ch. 6.2 - Determining a Distance A woman standing on a hill...Ch. 6.2 - Height of a Tower A water tower is located 325 ft...Ch. 6.2 - Prob. 56ECh. 6.2 - Determining a Distance If both cars in Exercise 62...Ch. 6.2 - Height of a Balloon A hot-air balloon is floating...Ch. 6.2 - Height of a Mountain To estimate the height of a...Ch. 6.2 - Height of Cloud Cover To measure the height of the...Ch. 6.2 - Distance to the Sun When the moon is exactly half...Ch. 6.2 - Distance to the Moon To find the distance to the...Ch. 6.2 - Prob. 63ECh. 6.2 - Parallax To find the distance to nearby stars, the...Ch. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.3 - If the angle is in standard position and P(x, y)...Ch. 6.3 - The sign of a trigonometric function of depends...Ch. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Prob. 41ECh. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - Prob. 45ECh. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - Prob. 49ECh. 6.3 - Prob. 50ECh. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.3 - Prob. 59ECh. 6.3 - Prob. 60ECh. 6.3 - Prob. 61ECh. 6.3 - Prob. 62ECh. 6.3 - Height of a Rocket A rocket fired straight up is...Ch. 6.3 - Rain Gutter A rain gutter is to be constructed...Ch. 6.3 - Wooden Beam A rectangular beam is to be cut from a...Ch. 6.3 - Prob. 66ECh. 6.3 - Throwing a Shot Put The range R and height H of a...Ch. 6.3 - Sledding The time in seconds that it takes for a...Ch. 6.3 - Beehives In a beehive each cell is a regular...Ch. 6.3 - Turning a Comer A steel pipe is being carried down...Ch. 6.3 - Rainbows Rainbows are created when sunlight of...Ch. 6.3 - Prob. 72ECh. 6.3 - Prob. 73ECh. 6.4 - Prob. 1ECh. 6.4 - In the triangle shown we can find the angle as...Ch. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Leaning Ladder A 20-ft ladder is leaning against a...Ch. 6.4 - Prob. 38ECh. 6.4 - Height of the Space Shuttle An observer views the...Ch. 6.4 - Height of a Pole A 50-ft pole casts a shadow as...Ch. 6.4 - Height of a Balloon A 680-ft rope anchors a...Ch. 6.4 - View from a Satellite The figures on the next page...Ch. 6.4 - Surfing the Perfect Wave For a wave to be...Ch. 6.4 - Prob. 44ECh. 6.5 - In triangle ABC with sides a, b, and c the Law of...Ch. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Prob. 24ECh. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Prob. 28ECh. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Tracking a Satellite The path of a satellite...Ch. 6.5 - Flight of a Plane A pilot is flying over a...Ch. 6.5 - Prob. 35ECh. 6.5 - Distance Across a Lake Points A and B are...Ch. 6.5 - The Leaning Tower of Pisa The bell lower of the...Ch. 6.5 - Radio Antenna A short-wave radio antenna is...Ch. 6.5 - Height of a Tree A tree on a hillside casts a...Ch. 6.5 - Length of a Guy Wire A communications tower is...Ch. 6.5 - Calculating a Distance Observers at P and Q are...Ch. 6.5 - Calculating an Angle A water tower 30 m tall is...Ch. 6.5 - Distances to Venus The elongation of a planet is...Ch. 6.5 - Soap Bubbles When two bubbles cling together in...Ch. 6.5 - Prob. 45ECh. 6.6 - For triangle ABC with sides a, b, and c the Law of...Ch. 6.6 - In which of the following cases must the Law of...Ch. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Prob. 8ECh. 6.6 - Prob. 9ECh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Prob. 12ECh. 6.6 - Prob. 13ECh. 6.6 - Prob. 14ECh. 6.6 - Prob. 15ECh. 6.6 - Prob. 16ECh. 6.6 - Prob. 17ECh. 6.6 - Prob. 18ECh. 6.6 - Prob. 19ECh. 6.6 - Prob. 20ECh. 6.6 - Prob. 21ECh. 6.6 - Prob. 22ECh. 6.6 - Prob. 23ECh. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - Prob. 26ECh. 6.6 - Prob. 27ECh. 6.6 - Prob. 28ECh. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - Prob. 33ECh. 6.6 - Prob. 34ECh. 6.6 - Prob. 35ECh. 6.6 - Prob. 36ECh. 6.6 - Prob. 37ECh. 6.6 - Prob. 38ECh. 6.6 - Surveying To find the distance across a small...Ch. 6.6 - Geometry A parallelogram has sides of lengths 3...Ch. 6.6 - Calculating Distance Two straight roads diverge at...Ch. 6.6 - Calculating Distance A car travels along a...Ch. 6.6 - Dead Reckoning A pilot flies in a straight path...Ch. 6.6 - Navigation Two boats leave the same port at the...Ch. 6.6 - Prob. 45ECh. 6.6 - Navigation Airport B is 300 mi from airport A at a...Ch. 6.6 - Triangular Field A triangular field has sides of...Ch. 6.6 - Towing a Barge Two tugboats that are 120 ft apart...Ch. 6.6 - Flying Kites A boy is flying two kites at the same...Ch. 6.6 - Securing a Tower A 125-ft tower is located on the...Ch. 6.6 - Cable Car A steep mountain is inclined 74 to the...Ch. 6.6 - CN Tower The CN Tower in Toronto, Canada, is the...Ch. 6.6 - Land Value Land in downtown Columbia is valued at...Ch. 6.6 - Prob. 54ECh. 6 - Prob. 1RCCCh. 6 - Prob. 2RCCCh. 6 - Prob. 3RCCCh. 6 - Prob. 4RCCCh. 6 - Prob. 5RCCCh. 6 - Prob. 6RCCCh. 6 - Prob. 7RCCCh. 6 - Prob. 8RCCCh. 6 - Prob. 9RCCCh. 6 - Prob. 10RCCCh. 6 - Prob. 11RCCCh. 6 - Prob. 12RCCCh. 6 - Prob. 13RCCCh. 6 - Prob. 14RCCCh. 6 - Prob. 15RCCCh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - 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(a)...Ch. 6 - Find tan + sin for the angle shown.Ch. 6 - Express the lengths a and b shown in the figure in...Ch. 6 - If cos=13 and is in Quadrant III, find tan cot ...Ch. 6 - Prob. 8TCh. 6 - Express tan in terms of sec for in Quadrant II.Ch. 6 - The base of the ladder in the figure is 6 ft from...Ch. 6 - Express in each figure in terms of x. (a) (b)Ch. 6 - Find the exact value of cos(tan1910).Ch. 6 - Prob. 13TCh. 6 - Find the side labeled x or the angle labeled . 14.Ch. 6 - Find the side labeled x or the angle labeled . 15.Ch. 6 - Prob. 16TCh. 6 - Prob. 17TCh. 6 - Prob. 18TCh. 6 - Refer to the figure below. (a) Find the area of...Ch. 6 - Refer to the figure below. (a) Find the angle...Ch. 6 - Two wires tether a balloon to the ground, as...Ch. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Determining a Distance A surveyor on one side of a...Ch. 6 - Height of a Cliff To measure the height of an...Ch. 6 - Height of a Mountain To calculate the height h of...Ch. 6 - Determining a Distance A surveyor has determined...Ch. 6 - Surveying Building Lots A surveyor surveys two...Ch. 6 - Prob. 8P
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