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Let AABC be a triangle with sides a, b and c and an angle Y = 2(ACB) between the sides a and b. Prove that the Law of Cosines holds truc c²=a² +6²-2ab cos y. Hint: Introduce a coordinate system so that y is in a standard position, then express coordinates and y of the vertex A(x, y) in terms of y and the use the distance formula to compute c.

Let AABC be a triangle with sides a, b and c and an angle Y = 2(ACB) between the sides a and b. Prove that the Law of Cosines holds truc c²=a² +6²-2ab cos y. Hint: Introduce a coordinate system so that y is in a standard position, then express coordinates and y of the vertex A(x, y) in terms of y and the use the distance formula to compute c.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 47PS
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Let AABC be a triangle with sides a, b and c and an angle Y = 2(ACB) between the sides a and b. Prove that the Law of Cosines holds true c²a² +6²-2ab cos y. Hint: Introduce a coordinate system so that y is in a standard position, then express coordinates and y of the vertex A(x, y) in terms of y and the use the distance formula to compute c.
Transcribed Image Text:Let AABC be a triangle with sides a, b and c and an angle Y = 2(ACB) between the sides a and b. Prove that the Law of Cosines holds true c²a² +6²-2ab cos y. Hint: Introduce a coordinate system so that y is in a standard position, then express coordinates and y of the vertex A(x, y) in terms of y and the use the distance formula to compute c.
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