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The Cosine Rule

The Cosine Rule. What is to be learned?. How to calculate a side using the cosine rule How to calculate an angle using the cosine rule. Calculating a Side. Formulas a 2 = b 2 + c 2 – 2bc CosA (on formula sheet) b? b 2 = a 2 + c 2 – 2ac CosB

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The Cosine Rule

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  1. The Cosine Rule

  2. What is to be learned? • How to calculate a side using the cosine rule • How to calculate an angle using the cosine rule

  3. Calculating a Side Formulas a2 =b2 + c2 – 2bc CosA (on formula sheet) b? b2 =a2 + c2 – 2ac CosB c2 =a2 + b2 – 2ab CosC Nasty formula but no need to rearrange

  4. a2 =b2 + c2 – 2bc CosA = 72 + 122 – 2 X 7 X 12 X Cos700 = 135.541 a2 = 135.541 a = √135.541 = 11.6 cm A 7cm 700 12cm C x B

  5. The Cosine Rule Calculating a Side a2 =b2 + c2 – 2bc CosA (on formula sheet) b? b2 =a2 + c2 – 2ac CosB c2 =a2 + b2 – 2ab CosC Nasty formula but no need to rearrange

  6. c2 =a2 + b2 – 2ab CosC = 142 + 82 – 2 X 14 X 8 X Cos750 = 202.02 c2 = 202.02 c = √202.02 = 14.2 cm all at once A 8cm C x 750 14cm B remember square root

  7. Calculating Angle Formula cosA = b2 + c2 – a2 2bc on formula sheet cosB = a2 + c2 – b2 2ac cosC = a2 + b2 – c2 2ab

  8. cosC = a2 + b2 – c2 2ab =132 + 92 – 142 2 x 13 x 9 = 54 234 = 0.2308 C = 76.70 (using correct button on calc) A 9cm 14cm C x 13cm B

  9. Calculating Angle Formula cosA = b2 + c2 – a2 2bc on formula sheet cosB = a2 + c2 – b2 2ac cosC = a2 + b2 – c2 2ab

  10. each line separately cosB = a2 + c2 – b2 2ac =132 + 152 – 102 2 x 13 x 15 = 294 390 = 0.7538 B = 41.10 (using correct button on calc) A 10cm 15cm C 13cm x B

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