To determine To solve: The triangle if a = 1.78 , b = 6.04 and c = 4.80 . 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 = 1.78 , b = 6.04 and c = 4.80 . 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 1.78 for a , 6.04 for b and 4.80 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 6.04 2 = 1.78 2 + 4.80 2 − 2 ( 1.78 ) ( 4.80 ) cos B 2 ( 1.78 ) ( 4.80 ) cos B = 1.78 2 + 4.80 2 − 6.04 2 cos B = 1

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 9.6, Problem 18E

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To solve: The triangle if a=1.78,b=6.04 and c=4.80.

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Chapter 9.6, Problem 17E

Chapter 9.6, Problem 19E

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