Explanation Formula used: Law of cosines: Consider the following triangle as shown below: Let a, b and c be the sides of the triangle, then the law of cosines is given by: 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 magnitude of a = 0.2433 , b = 0.2635 and c = 0.1538 . Sketch the graph of the triangle with known measures as shown below in Figure 1. From Figure 1, it is observed that the three sides of the triangle is known. So, directly solve the angle opposite to the largest side, using law of cosines. The largest side is b here. So, obtain the angle B as follows. Substitute 0.2433 for a , 0.2635 for b and 0.1538 for c in b 2 = a 2 + c 2 − 2 a c cos B . b 2 = a 2 + c 2 − 2 a c cos B 0.2635 2 = 0.2433 2 + 0.1538 2 − 2 ( 0.2433 ) ( 0.1538 ) cos B 2 ( 0.2433 ) ( 0.1538 ) cos B = 0.2433 2 + 0.1538 2 − 0.2635 2 cos B = 0

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Chapter 9.6, Problem 10E

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To solve: The triangle if a=0.2433,b=0.2635 and c=0.1538.

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Chapter 9.6, Problem 9E

Chapter 9.6, Problem 11E

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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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The triangle if a = 0.2433 , b = 0.2635 and c = 0.1538 .

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To solve: The triangle if a=0.2433,b=0.2635 and c=0.1538.

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