8-7 Law of Cosines Law of Cosines: Allows us to solve a triangle when the Law of Sines cannot be used. Theorem 8.9: Let ∆ABC be any triangle with a, b,

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Presentation transcript:

8-7 Law of Cosines Law of Cosines: Allows us to solve a triangle when the Law of Sines cannot be used. Theorem 8.9: 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 A B C a b c

Example 1 In ∆DEF, e = 19, f = 28, and m∠D = 49. Find d.

Example 2 In ∆TVW, v = 18, t = 24, and w = 30. Find m∠W.

Concept Summary To Solve Given Begin by using Right Triangle Two legs Tangent Leg and hypotenuse Sine or cosine Angle and hypotenuse Angle and a leg Sine, cosine, or tangent Any Triangle Two angles and any side Law of Sines Two sides and the angle opposite one of them Two sides and the included angle Law of Cosines Three sides

Example 3 Solve ∆XYZ for x = 10, y = 11, and z = 12.

Example 4 Refer to the picture on p. 482 An architect is designing a playground in the shape of a quadrilateral. Find the perimeter of the playground to the nearest tenth. 1) Use Pythagorean Theorem to find JL JL = 22.2 2) Use Law of Cosines (JL, KJ, ∠LJK) to find KL. KL = 12.4 Answer: 58.4 m

Homework #55 p. 482 8-14 even, 16-22, 25-35 odd, 41, 43-44