Stitz-Zeager_College_Algebra_e-book

We graph it below x2 x 2 y 2 xy 2 2 x y2 the

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Unformatted text preview: uares. 1 2 (a + b + c) = a+b+c 2. To 778 Applications of Trigonometry complete the proof, we note that (s − a) = = = Similarly, we find (s − b) = a+c−b 2 a+b+c −a 2 a + b + c − 2a 2 b+c−a 2 and (s − c) = a+b−c 2. Hence, we get (b + c − a) (a + c − b) (a + b − c) (a + b + c) · · · 2 2 2 2 = (s − a)(s − b)(s − c)s A2 = so that A = s(s − a)(s − b)(s − c) as required. Example 11.3.3. Find the area enclosed of the triangle in Example 11.3.1 number 2. Solution. We are given a = 4, b = 7 and c = 5. Using these values, we find s = 1 (4 + 7 + 5) = 8, 2 (s − a) = 8 − 4 = 4, (s − b) = 8 − 7 = 1 and (s √ c) = 8√ 5 = 3. Using Heron’s Formula, we get − − A = s(s − a)(s − b)(s − c) = (8)(4)(1)(3) = 96 = 4 6 ≈ 9.80 square units. 11.3 The Law of Cosines 11.3.1 779 Exercises 1. Use the Law of Cosines to find the remaining side(s) and angle(s) if possible. (a) a = 7, b = 12, γ = 59.3◦ (f) a = 7, b = 10, c = 13 (b) α = 104◦ , b = 25, c = 37 (g) a = 1, b = 2, c = 5 (c) a = 153, β = 8.2◦ , (d) a...
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