Explanation Given information: Given triangle A B C with vertices A ( − 2 , 1 ) , B ( 5 , 3 ) , and C ( 3 , 6 ) Formula used: Distance formula to find length of all sides of the triangle given the coordinates of the vertices. If the coordinates are ( x 1 , y 1 ) and ( x 2 , y 2 ) then the general formula for distance d d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Use the law of cosines to find two of the angles among the three a 2 = b 2 + c 2 − 2 b c cos A ∴ cos A = b 2 + c 2 − a 2 2 b c Similarly b 2 = a 2 + c 2 − 2 a c cos B ∴ cos B = a 2 + c 2 − b 2 2 a c Find the third angle using angle sum formula C = 180 ∘ − ( A + B ) Finding all sides and all angles forms the solution Calculation: Given triangle A B C with vertices A ( − 2 , 1 ) , B ( 5 , 3 ) , and C ( 3 , 6 ) We shall find each side of the triangle and then the corresponding angles Let the side lengths be a = B C , b = A C and c = A B a = B C = ( 3 − 5 ) 2 + ( 6 − 3 ) 2 = 13 = 3.60 b = A C = ( 3 − ( − 2 ) ) 2 + ( 6 − 1 ) 2 = 50 = 7

Pearson eText for College Algebra and Trigonometry -- Instant Access (Pearson+)

4th Edition

ISBN: 9780137399048

Author: J. S. Ratti, Marcus McWaters

Publisher: PEARSON+

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 7.2, Problem 87E

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Solve triangle ABC with vertices A(−2,1),B(5,3),and C(3,6).

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Chapter 7.2, Problem 86E

Chapter 7.2, Problem 88E

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Pearson eText for College Algebra and Trigonometry -- Instant Access (Pearson+)

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - True or False.A triangle is uniquely determined if...Ch. 7.1 - True or False.In a triangle ABC,sinAsinB=ab .Ch. 7.1 - True or False.The Law of Sines cannot be used to...Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - 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Prob. 57E Ch. 7.3 - Prob. 58E Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Prob. 61E Ch. 7.3 - In Exercises, round your answer (in square feet or...Ch. 7.3 - Prob. 63E Ch. 7.3 - Prob. 64E Ch. 7.3 - Prob. 65E Ch. 7.3 - Prob. 66E Ch. 7.3 - Prob. 67E Ch. 7.3 - Prob. 68E Ch. 7.3 - Prob. 69E Ch. 7.3 - Prob. 70E Ch. 7.3 - Exercises deal with a regular polygon.For n3, a...Ch. 7.3 - Prob. 72E Ch. 7.3 - Exercises deal with a regular polygon.For n3, a...Ch. 7.3 - Exercises deal with a regular polygon.For n3, a...Ch. 7.3 - Prob. 75E Ch. 7.3 - Prob. 76E Ch. 7.3 - Exercises deal with a regular polygon.For n3, a...Ch. 7.3 - Exercises deal with a regular polygon.For n3, a...Ch. 7.3 - Prob. 79E Ch. 7.3 - Prob. 80E Ch. 7.3 - Prob. 81E Ch. 7.3 - Prob. 82E Ch. 7.3 - Prob. 83E Ch. 7.3 - Prob. 84E Ch. 7.3 - Prob. 85E Ch. 7.3 - Prob. 86E Ch. 7.3 - Prob. 87E Ch. 7.3 - Prob. 88E Ch. 7.3 - Prob. 89E Ch. 7.3 - Prob. 90E Ch. 7.3 - Prob. 91E Ch. 7.3 - Prob. 92E Ch. 7.3 - Prob. 93E Ch. 7.3 - Prob. 94E Ch. 7.3 - Prob. 95E Ch. 7.3 - Prob. 96E Ch. 7.3 - Prob. 97E Ch. 7.3 - Prob. 98E Ch. 7.3 - Prob. 99E Ch. 7.3 - Prob. 100E Ch. 7.3 - Prob. 101E Ch. 7.3 - Prob. 102E Ch. 7.3 - Prob. 103E Ch. 7.3 - Prob. 104E Ch. 7.4 - A vector is a quantity that is characterized by a...Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - If v is a nonzero vector, then the unit vector u...Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - Prob. 35E Ch. 7.4 - Prob. 36E Ch. 7.4 - 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Prob. 53E Ch. 7.6 - Prob. 54E Ch. 7.6 - Prob. 55E Ch. 7.6 - Prob. 56E Ch. 7.6 - Prob. 57E Ch. 7.6 - Prob. 58E Ch. 7.6 - Prob. 59E Ch. 7.6 - Prob. 60E Ch. 7.6 - Prob. 61E Ch. 7.6 - Prob. 62E Ch. 7.6 - Prob. 63E Ch. 7.6 - Prob. 64E Ch. 7.6 - Prob. 65E Ch. 7.6 - Prob. 66E Ch. 7.6 - Prob. 67E Ch. 7.6 - Prob. 68E Ch. 7.6 - Prob. 69E Ch. 7.6 - Prob. 70E Ch. 7.6 - Prob. 71E Ch. 7.6 - Prob. 72E Ch. 7.6 - Prob. 73E Ch. 7.6 - Prob. 74E Ch. 7.6 - Prob. 75E Ch. 7.6 - Prob. 76E Ch. 7.6 - Prob. 77E Ch. 7.6 - Prob. 78E Ch. 7.6 - Prob. 79E Ch. 7.6 - Prob. 80E Ch. 7.6 - Prob. 81E Ch. 7.6 - Prob. 82E Ch. 7.6 - Prob. 83E Ch. 7.6 - Prob. 84E Ch. 7.6 - Prob. 85E Ch. 7.6 - Prob. 86E Ch. 7.6 - Prob. 87E Ch. 7.6 - In Exercises, determine the position of the hand...Ch. 7.6 - Prob. 89E Ch. 7.6 - Prob. 90E Ch. 7.6 - Prob. 91E Ch. 7.6 - Prob. 92E Ch. 7.6 - Prob. 93E Ch. 7.6 - Prob. 94E Ch. 7.6 - Prob. 95E Ch. 7.6 - Prob. 96E Ch. 7.6 - Prob. 97E Ch. 7.6 - Prob. 98E Ch. 7.6 - Prob. 99E Ch. 7.6 - Prob. 100E Ch. 7.6 - Prob. 101E Ch. 7.6 - Prob. 102E Ch. 7.6 - Prob. 103E Ch. 7.6 - Prob. 104E Ch. 7.6 - Prob. 105E Ch. 7.6 - Prob. 106E Ch. 7.6 - Prob. 107E Ch. 7.6 - Prob. 108E Ch. 7.6 - Prob. 109E Ch. 7.6 - Prob. 110E Ch. 7.6 - Prob. 111E Ch. 7.6 - Prob. 112E Ch. 7.6 - Prob. 113E Ch. 7.6 - Prob. 114E Ch. 7.6 - Prob. 115E Ch. 7.6 - Prob. 116E Ch. 7.6 - Prob. 117E Ch. 7.6 - Prob. 118E Ch. 7.6 - Prob. 119E Ch. 7.6 - Prob. 120E Ch. 7.6 - Prob. 121E Ch. 7.6 - Prob. 122E Ch. 7.6 - Prob. 123E Ch. 7.6 - Prob. 124E Ch. 7.6 - Prob. 125E Ch. 7.6 - Prob. 126E Ch. 7.6 - Prob. 127E Ch. 7.6 - Prob. 128E Ch. 7.6 - Prob. 129E Ch. 7.6 - Prob. 130E Ch. 7.6 - Prob. 131E Ch. 7.6 - Prob. 132E Ch. 7.6 - Prob. 133E Ch. 7.6 - Prob. 134E Ch. 7.6 - Prob. 135E Ch. 7.6 - Prob. 136E Ch. 7.6 - Prob. 137E Ch. 7.6 - Prob. 138E Ch. 7.6 - Prob. 139E Ch. 7.6 - Prob. 140E Ch. 7.6 - Prob. 141E Ch. 7.6 - Prob. 142E Ch. 7.7 - Prob. 1E Ch. 7.7 - If and then the polar form of z is z = _________.Ch. 7.7 - Prob. 3E Ch. 7.7 - Prob. 4E Ch. 7.7 - Prob. 5E Ch. 7.7 - Prob. 6E Ch. 7.7 - Prob. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - Prob. 9E Ch. 7.7 - Prob. 10E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Prob. 21E Ch. 7.7 - Prob. 22E Ch. 7.7 - Prob. 23E Ch. 7.7 - Prob. 24E Ch. 7.7 - Prob. 25E Ch. 7.7 - In Exercises, write each complex number in polar...Ch. 7.7 - Prob. 27E Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Prob. 36E Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7.7 - Prob. 41E Ch. 7.7 - Prob. 42E Ch. 7.7 - Prob. 43E Ch. 7.7 - Prob. 44E Ch. 7.7 - Prob. 45E Ch. 7.7 - Prob. 46E Ch. 7.7 - Prob. 47E Ch. 7.7 - Prob. 48E Ch. 7.7 - Prob. 49E Ch. 7.7 - Prob. 50E Ch. 7.7 - Prob. 51E Ch. 7.7 - Prob. 52E Ch. 7.7 - Prob. 53E Ch. 7.7 - Prob. 54E Ch. 7.7 - Prob. 55E Ch. 7.7 - Prob. 56E Ch. 7.7 - Prob. 57E Ch. 7.7 - Prob. 58E Ch. 7.7 - Prob. 59E Ch. 7.7 - Prob. 60E Ch. 7.7 - Prob. 61E Ch. 7.7 - Prob. 62E Ch. 7.7 - Prob. 63E Ch. 7.7 - Prob. 64E Ch. 7.7 - Prob. 65E Ch. 7.7 - Prob. 66E Ch. 7.7 - Prob. 67E Ch. 7.7 - Prob. 68E Ch. 7.7 - Prob. 69E Ch. 7.7 - In Exercises, use DeMoivre’s Theorem to find the...Ch. 7.7 - Prob. 71E Ch. 7.7 - Prob. 72E Ch. 7.7 - Prob. 73E Ch. 7.7 - Prob. 74E Ch. 7.7 - Prob. 75E Ch. 7.7 - Prob. 76E Ch. 7.7 - Prob. 77E Ch. 7.7 - Prob. 78E Ch. 7.7 - Prob. 79E Ch. 7.7 - Prob. 80E Ch. 7.7 - Prob. 81E Ch. 7.7 - Prob. 82E Ch. 7.7 - Prob. 83E Ch. 7.7 - Prob. 84E Ch. 7.7 - Prob. 85E Ch. 7.7 - Prob. 86E Ch. 7.7 - Prob. 87E Ch. 7.7 - Prob. 88E Ch. 7.7 - Prob. 89E Ch. 7.7 - Prob. 90E Ch. 7.7 - Prob. 91E Ch. 7.7 - Prob. 92E Ch. 7.7 - In Exercises, find all complex solutions of each...Ch. 7.7 - Prob. 94E Ch. 7.7 - Prob. 95E Ch. 7.7 - Prob. 96E Ch. 7.7 - Prob. 97E Ch. 7.7 - Prob. 98E Ch. 7.7 - Prob. 99E Ch. 7.7 - Prob. 100E Ch. 7.7 - Prob. 101E Ch. 7.7 - Prob. 102E Ch. 7.7 - Prob. 103E Ch. 7.7 - Prob. 104E Ch. 7.7 - Prob. 105E Ch. 7.7 - Prob. 106E Ch. 7.7 - Prob. 107E Ch. 7.7 - Prob. 108E Ch. 7.7 - Prob. 109E Ch. 7.7 - Prob. 110E Ch. 7.7 - Prob. 111E Ch. 7.7 - Prob. 112E Ch. 7.7 - Prob. 113E Ch. 7.7 - Prob. 114E Ch. 7.7 - Prob. 115E Ch. 7.7 - Prob. 116E Ch. 7.7 - Prob. 117E Ch. 7.7 - Prob. 118E Ch. 7.7 - Prob. 119E Ch. 7.7 - Prob. 120E Ch. 7 - In Exercises, solve right triangle ABC with right...Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - In Exercises, solve right triangle ABC with right...Ch. 7 - Prob. 10RE Ch. 7 - In Exercises, use the Law of sines to solve each...Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Repeat Exercise 19 for c=20 and B=150 .Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Prob. 46RE Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Prob. 53RE Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Prob. 57RE Ch. 7 - In Exercises, plot each point in polar coordinates...Ch. 7 - In Exercises, convert the rectangular coordinates...Ch. 7 - In Exercises, convert the rectangular coordinates...Ch. 7 - In Exercises, convert the rectangular coordinates...Ch. 7 - In Exercises, convert the rectangular coordinates...Ch. 7 - Prob. 63RE Ch. 7 - Prob. 64RE Ch. 7 - Prob. 65RE Ch. 7 - Prob. 66RE Ch. 7 - Prob. 67RE Ch. 7 - Prob. 68RE Ch. 7 - Prob. 69RE Ch. 7 - Prob. 70RE Ch. 7 - Prob. 71RE Ch. 7 - Prob. 72RE Ch. 7 - Prob. 73RE Ch. 7 - Prob. 74RE Ch. 7 - Prob. 75RE Ch. 7 - Prob. 76RE Ch. 7 - Prob. 77RE Ch. 7 - Prob. 78RE Ch. 7 - Prob. 79RE Ch. 7 - Prob. 80RE Ch. 7 - Prob. 81RE Ch. 7 - Prob. 82RE Ch. 7 - Prob. 83RE Ch. 7 - Prob. 84RE Ch. 7 - Prob. 85RE Ch. 7 - Prob. 86RE Ch. 7 - Prob. 87RE Ch. 7 - Prob. 88RE Ch. 7 - Prob. 89RE Ch. 7 - Prob. 90RE Ch. 7 - In Exercises, find all complex roots.Write your...Ch. 7 - Prob. 92RE Ch. 7 - Prob. 93RE Ch. 7 - Prob. 94RE Ch. 7 - Prob. 95RE Ch. 7 - Prob. 96RE Ch. 7 - Prob. 97RE Ch. 7 - Prob. 98RE Ch. 7 - Prob. 99RE Ch. 7 - Prob. 100RE Ch. 7 - Prob. 1PTA Ch. 7 - Prob. 2PTA Ch. 7 - Prob. 3PTA Ch. 7 - Prob. 4PTA Ch. 7 - Prob. 5PTA Ch. 7 - Prob. 6PTA Ch. 7 - Prob. 8PTA Ch. 7 - Prob. 9PTA Ch. 7 - Prob. 10PTA Ch. 7 - Prob. 11PTA Ch. 7 - Prob. 12PTA Ch. 7 - Prob. 13PTA Ch. 7 - Prob. 14PTA Ch. 7 - Prob. 15PTA Ch. 7 - Prob. 16PTA Ch. 7 - Prob. 17PTA Ch. 7 - Prob. 18PTA Ch. 7 - Prob. 19PTA Ch. 7 - Prob. 20PTA Ch. 7 - Prob. 1PTB Ch. 7 - Prob. 2PTB Ch. 7 - Prob. 3PTB Ch. 7 - Prob. 4PTB Ch. 7 - Prob. 5PTB Ch. 7 - Prob. 6PTB Ch. 7 - Prob. 7PTB Ch. 7 - Prob. 8PTB Ch. 7 - Prob. 9PTB Ch. 7 - Prob. 10PTB Ch. 7 - Prob. 11PTB Ch. 7 - Prob. 12PTB Ch. 7 - Prob. 13PTB Ch. 7 - Prob. 14PTB Ch. 7 - Prob. 15PTB Ch. 7 - Prob. 16PTB Ch. 7 - Prob. 17PTB Ch. 7 - Prob. 18PTB Ch. 7 - Prob. 19PTB Ch. 7 - Prob. 20PTB Ch. 7 - Prob. 1CRE Ch. 7 - Prob. 2CRE Ch. 7 - Prob. 3CRE Ch. 7 - Prob. 4CRE Ch. 7 - Prob. 5CRE Ch. 7 - Prob. 6CRE Ch. 7 - Prob. 7CRE Ch. 7 - Prob. 8CRE Ch. 7 - Prob. 9CRE Ch. 7 - Prob. 10CRE Ch. 7 - Prob. 11CRE Ch. 7 - Prob. 12CRE Ch. 7 - Prob. 13CRE Ch. 7 - Prob. 14CRE Ch. 7 - Prob. 15CRE Ch. 7 - Use an identity to find the exact value of...Ch. 7 - Prob. 17CRE Ch. 7 - Prob. 18CRE Ch. 7 - Prob. 19CRE Ch. 7 - Prob. 20CRE

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Solve triangle ABC with vertices A ( − 2 , 1 ) , B ( 5 , 3 ) , and C ( 3 , 6 ) .

Solution Summary: The author explains how to solve triangle ABC with vertices A(-2,1),B(5,3),andC(3,6).

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Solve triangle ABC with vertices A(−2,1),B(5,3),and C(3,6).

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Chapter 7 Solutions