Math 20-1 Chapter 2 Trigonometry 2.4 The Cosine Law Teacher Notes

Math 20-1 Chapter 1 Sequences and Series 2.4 The Cosine Law Explain why the sine law cannot be used to solve each triangle. E D 85° F P Q R 15 J K L A B 28° 37° 115° C There is no known side opposite a known angle. There is no known angle opposite a known side There is no known angle and only one known side. There is no known angle opposite a known side. Adapted from McGraw-Hill Ryerson PreCalculus Digital Resources.

b2 b2 + c 2 -2bc cosA a 2 = a2 a2 + c 2 -2ac cosB b 2 = a2 a2 + b 2 -2ab cosC c 2 = SSS Given the measure of three sides. SAS Given the measure of two sides and one angle not opposite a side

D B C A ca b xb - x h 2.4.3

b 2 = a 2 + c 2 -2ac cosB = (230) 2 + (150) 2 - 2(230)(150)cos43 0 b = m a 2 = b 2 + c 2 -2bc cosA = (61) 2 + (43) 2 - 2(61)(43)cos38 0 a = 37.9 cm SAS Applying the Law of Cosines (to the nearest 10th) 2.4.4

SSS Finding an Angle Using the Law of Cosines (to the nearest degree) a 2 = b 2 + c 2 -2bc cosA 38 2 = (61)(43) cosA Determine the measure of angle A = -2(61)(43) cosA 2.4.5

85 2 = (64)(78) cosE Given triangle DEF, find. SSS Finding an Angle Using the Law of Cosines (to the nearest degree) 2.4.6

b 2 = (95) 2 + (200) 2 - 2(95)(200)cos50 b 2 ~ b = h h = The rope to the balloon is m Solving Two Triangles b Determine the length of the rope to the balloon. (to the nearest tenth) 2.4.7

When solving triangles, it is important to choose the most appropriate method. The choice depends on the given information. Place the letter of the appropriate method beside the given information. Solving Triangles Given Information Begin by using the method Three sides Three angles Two angles and any side Right triangle Two sides and the angle between them Two sides and the angle opposite one of the sides A. Primary trig ratio B. sine law C. cosine law D. none of the above C D B A C B SSS AAA AAS SAS SSA

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