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Pre-Calc Exam Notes 53

# Pre-Calc Exam Notes 53 - The Law of Tangents Section 2.3 53...

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The Law of Tangents Section 2.3 53 Example2.12 Can a triangle have the parts a = 6, b = 7, c = 9, A = 55 , B = 60 , and C = 65 ? Solution: Before using Mollweide’s equations, simpler checks are that the angles add up to 180 and that the smallest and largest sides are opposite the smallest and largest angles, respectively. In this case all those conditions hold. So check with Mollweide’s equation (2.22): a + b c = cos 1 2 ( A B ) sin 1 2 C 6 + 7 9 = cos 1 2 (55 60 ) sin 1 2 (65 ) 13 9 = cos ( 2 . 5 ) sin 32 . 5 1 . 44 = 1 . 86 Here the difference is far too large, so we conclude that there is no triangle with these parts. We will prove the Law of Tangents and Mollweide’s equations in Chapter 3, where we will be able to supply brief analytic proofs. 6 Exercises For Exercises 1-3, use the Law of Tangents to solve the triangle ABC . 1. a = 12, b = 8, C = 60 2. A = 30 , b = 4, c = 6 3. a = 7, B = 60 , c = 9 For Exercises 4-6, check if it is possible for a triangle to have the given parts.
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