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Warm up

Preliminary Activity. Notes. For Fun. Warm up. Activity. θ. USING THE COSINE RULE TO FIND A MISSING ANGLE. θ. θ. Back. Back. 1. The cosine ratio is the ratio of A adjacent B opposite C adjacent D opposite hypotenuse adjacent opposite hypotenuse

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Warm up

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

  2. Back Back 1. The cosine ratio is the ratio of AadjacentBoppositeC adjacentDopposite hypotenuse adjacent opposite hypotenuse 2. in the triangle sinθ is A12B 9 9 12 C 9 D12 15 15 3. Correct to four decimal places cos 53o 18' is A 0.5976 B 0.8018 C 0.6018 D 1.3416 4. If tanθ = 7 , then, to the nearest minute, θ = 5 A 54o27'B 54o28'C 16o22'D 16o23' 5. In the triangle, to the nearest minute, θ = A 38o29'B 38o30' C 38o3'D 51o30' 6. To one decimal place, x = A 20.5 B 19.1 C 19.2 D 15.0

  3. Back 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 a2 = b2 + c2 - 2bccosA b2 = a2 + c2 - 2accosB c2 = a2 + b2 - 2abcosC The cosine rule is used to find ·the third side given two sides and the included angle ·an angle given three sides Rearranging a2 = b2 + c2 - 2bccosA gives cosA = b2 + c2 - a2 2bc which is a more convenient form for finding angles. Likewise, cosB = a2 + c2 - b2and cosC = a2 + b2 - c2 2ac 2ab

  4. Back Back Use the cosine rule to find θ correct to the nearest degree. cosA = b2 + c2 - a2 2bc cosθ = 10.72 + 23.82 - 27.52 2 x 10.7 x 23.8 θ = 99o (to the nearest degree)

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

  6. Back Back $1 104 $1 096.50 $211.70 50.9% $17.25 8.5%

  7. Back Back

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