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Lesson 7-7. Law of Cosines. Transparency 7-7. 5-Minute Check on Lesson 7-6. Find each measure given the measures of ∆RST. Round all side measurements to the nearest tenth and angles to the nearest degree.. Find s, if m R = 63 °, m S = 38 °, and r = 52.

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## Lesson 7-7

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**Lesson 7-7**Law of Cosines**Transparency 7-7**5-Minute Check on Lesson 7-6 • Find each measure given the measures of ∆RST. Round all side measurements to the nearest tenth and angles to the nearest degree.. • Find s, if mR = 63°, mS = 38°, and r = 52. • Find mR, if mS = 122°, s = 10.8, and r = 5.2. • Solve ∆MNP described below. Round all side measurements to the nearest tenth and angles to the nearest degree. • mM = 50°, if mN = 32°, and m = 15. • n = 8.5, p = 10.8, and mP = 110°. • Find the perimeter of quadrilateral ABCD to the nearest tenth. 35.9 24° mP = 98°, n = 10.4, p = 19.4 mN = 48°, mM = 22°, m = 4.4 Standardized Test Practice: 70° 8 cm 54° B 27.6 29.8 32.0 34.6 A B C D Click the mouse button or press the Space Bar to display the answers.**Objectives**• Use the Law of Cosines to solve triangles • Solve problems by using the Law of Cosines**Vocabulary**• None new**Law of Cosines**A Let ∆ABC be any triangle with a, b and c representing the measures of the sides opposite the angles with measures A, B, and C respectively. Then the following equations are true: b c C B a a2 = b2 + c2 – 2bc cos A b2 = a2 + c2 – 2ac cos B c2 = a2 + b2 – 2ab cos C Law of Cosines can be used to solve triangles when the Law of Sines cannot be used Case 1: measures of two sides and their included angle (SAS) Case 2: measures of all three sides (SSS)**Answer:**Example1 Use the Law of Cosines since the measures of two sides and the included angle are known. Law of Cosines Simplify. Take the square root of each side. Use a calculator.**Answer:**Example 2**Answer:**Example 3 Law of Cosines Simplify. Subtract 754 from each side. Divide each side by –270. Solve for L. Use a calculator.**Answer:**Example 4**Determine whether the Law of Sines or the Law of Cosines**should be used first to solve Then solve Round angle measures to the nearest degree and side measures to the nearest tenth. Example 5 Since we know the measures of two sides and the included angle, use the Law of Cosines. Law of Cosines Take the square root of each side. Use a calculator.**Next, we can find If we decide to**find we can use either the Law of Sines or the Law of Cosines to find this value. In this case, we will use the Law of Sines. Example 5 cont Law of Sines Cross products Divide each side by 46.9.**Use the Angle Sum Theorem to find**Answer: Example 5 cont Take the inverse of each side. Use a calculator. Angle Sum Theorem Subtract 168 from each side.**Determine whether the Law of Sines or the Law of Cosines**should be used first to solve Then solve Round angle measures to the nearest degree and side measures to the nearest tenth. Answer: Example 6**Summary & Homework**• Summary: • The Law of Cosines can be used to solve non-right triangles when you know 1) the measures of two sides and the included angle (SAS) or 2) the measures of all three sides (SSS) • Homework: • pg 388-389; 11, 12, 19-21, 27-30, 42

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