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 Calculation: Let the vacuum cleaner starts from the point A. It travels 12.5 ft to the point B at the wall. That is, c = 12.5 ft . Then, it hits the wall and turns on 47 ° corner. Therefore, the angle B is 47 ° . Again it travels 15 ft to the point C. So, a = 15 ft . Sketch the graph of the triangle with known measures as shown below in Figure 1. From Figure 1, it is observed that the two sides and the included angle of the triangle is known. Use the law of cosines and obtain the distance between the point C and the starting point A as follows. That is, the side b , which is opposite to the angle B, has to be obtained. Substitute 15for a , 12.5 for c and 47 ° for B in b 2 = a 2 + c 2 − 2 a c cos B

11th Edition

ISBN: 9780134508290

Author: Evans

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 9.6, Problem 21E

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The distance of the vacuum cleaner from its starting point using law of cosines.

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Chapter 9.6, Problem 20E

Chapter 9.6, Problem 22E

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Chapter 9 Solutions

EBK BASIC TECHNICAL MATHEMATICS

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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