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Using the Cosine Rule to Find Missing Angles: Warm-up Activity Guide

This preliminary activity focuses on using the cosine rule to find missing angles in triangles. It provides examples and questions to help learners understand the cosine ratio and its applications in non-right-angled triangles. Through various exercises, participants will explore the relationship between sides and angles, learn to rearrange the cosine rule formula, and apply it to calculate missing angles accurately to the nearest degree. It's an engaging way to enhance your trigonometry skills!

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Using the Cosine Rule to Find Missing Angles: Warm-up Activity Guide

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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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