Explanation Formula used: For any triangle with sides a, b and c , opposite angles A , B and C respectively, the law of Cosines and law of Sine’s can be defined as follows. Law of cosines: a 2 = b 2 + c 2 − 2 b c cos A This can be also written as follows. b 2 = a 2 + c 2 − 2 a c cos B c 2 = a 2 + b 2 − 2 a b cos C Law of sines: a sin A = b sin B = c sin C Calculation: Given that, the radii of the circlesare24 in., 32 in. and 42 in. respectively. Join the centers of the circles and form a triangle. Sketch the graph of the given data with known measures as shown below in Figure 1. From Figure 1, it is observed that θ is the largest angle of the triangle. Both the other angles are acute angles. The length a is 42 + 24 = 66 in , length b is 24 + 32 = 56 in and length c is 42 + 32 = 74 in . Use the law of cosines and the angle θ can be obtained as follows. Substitute 66for a , 56 for b and 74 for c in c 2 = a 2 + b 2 − 2 a b cos C

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 9.6, Problem 26E

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The largest angle of the triangle formed by joining the centers of the 3 circles.

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Chapter 9.6, Problem 25E

Chapter 9.6, Problem 27E

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Chapter 9 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 9.1 - For the vectors in Example 2, show that R = B + C...Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E

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