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Pre Calculus 8.2/8.3 Warm Up The Law of Sines & Cosines Find the missing segment lengths and angles of the triangles. 1. B a 106.2 61.7º C 2. b A d F E 23 13 D Pre Calculus 8.2/8.3 NOTES The Law of Sines & Cosines OBJECTIVES: To use the law of sines and cosines to find unknown parts of a triangle. Solving oblique triangles Oblique triangle: The law of sines The Law of Sines In any triangle ABC, The sides are proportional to the sines of the opposite angles Solving Triangles (AAS and ASA) 1. In ∆EFG, e = 4.56, < E = 43º, and < G = 57º. Solve the triangle. 2. During a rescue mission, a Marine fighter pilot receives data on an unidentified aircraft from an AWACS plane and is instructed to intercept the aircraft. The diagram below appears on the screen, but before the distance to the point of interception appears on the screen, communications are jammed. Fortunately, the pilot remembers the law of sines. How far must the pilot fly? Z 115º X 500km 27º (unidentified aircraft) Y (pilot) Solving tiangles (SSA) 3. In ∆QRS, q = 15, r = 28 and Q = 43.6º. Solve the triangle. 4. In ∆XYZ, x = 23.5, y = 9.8, and X = 39.7º. Solve the triangle. The Law of Cosines The Law of Cosines In any triangle ABC, The square of a side is the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the included angle. Solving Triangles (SAS) 5. Solve ∆ABC if a = 32, c = 48, and B = 125.2º. Solving Triangles (SSS) 6. Solve ∆RST if r = 3.5, s = 4.7, and t = 2.8. 8. In ∆ABC, three measures are given. Determine which law to use when solving the triangle. a) a = 14, b = 23, c = 10 b) a = 207, B = 43.8º, C = 57.6º c) A = 112º, C = 37º, a = 84.7 d) B = 101º, a = 960, c = 1042 e) b = 17.26, a = 27.29, A = 39º f) A = 61º, B = 39º, C = 80º