Warm up Notes Preliminary Activity Activity For Fun USING THE COSINE RULE TO FIND A MISSING ANGLE θ θ θ

Back 1. The cosine ratio is the ratio of A adjacentB oppositeC adjacent D opposite hypotenuse adjacent opposite hypotenuse 2. in the triangle sinθ is A 12B C 9 D Correct to four decimal places cos 53 o 18 ' is A B C D If tanθ = 7, then, to the nearest minute, θ = 5 A 54 o 27 ' B 54 o 28 ' C 16 o 22 ' D 16 o 23' 5. In the triangle, to the nearest minute, θ = A 38 o 29 ' B 38 o 30 ' C 38 o 3'D 51 o 30 ' 6. To one decimal place, x = A 20.5B 19.1 C 19.2D 15.0

Back The cosine rule is another method used to find the sides and angles in non-right-angled triangles. The cosine rule: In any triangle ABC, with sides and angles as shown a 2 = b 2 + c 2 - 2bccosA b 2 = a 2 + c 2 - 2accosB c 2 = a 2 + b 2 - 2abcosC The cosine rule is used to find ·the third side given two sides and the included angle ·an angle given three sides Rearranging a 2 = b 2 + c 2 - 2bccosA gives cosA = b 2 + c 2 - a 2 2bc which is a more convenient form for finding angles. Likewise, cosB = a 2 + c 2 - b 2 and cosC = a 2 + b 2 - c 2 2ac 2ab

Back Use the cosine rule to find θ correct to the nearest degree. cosA = b 2 + c 2 - a 2 2bc cosθ = x 10.7 x 23.8 θ = 99 o (to the nearest degree)

Back 41.7% 56.3% 75.7% Complete exercise 5-07 Questions 1, 2, 4, 6, 8, 10, 12

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