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The Cosine Rule

The Cosine Rule. Monday 6 th October 2014. Labeling you triangle. It is important that you label correctly. Angles are represented by capital letters and lengths are represented by lower case letters. B. Each angle will correspond t o the length opposite. c. a. A. C. b.

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The Cosine Rule

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  1. The Cosine Rule Monday 6th October 2014

  2. Labeling you triangle • It is important that you label correctly. Angles are represented by capital letters and lengths are represented by lower case letters. B Each angle will correspond to the length opposite. c a A C b

  3. Trigonometry in Real Life • https://www.youtube.com/watch?v=WehHFJki9yQ

  4. The cosine Rule • a2=b2+c2-2bc cos A • We use this formula to calculate a missing length in a triangle. C Firstly label your triangle. Then you need to substitute the values into the formula: a2= 132+72 – 2×13×7×cos76 b 13 cm a x Now you need your calculator. Make sure it is in degree mode! 76° a2= 67.9716977384 a= 8.24449499596 a=8.24cm A B 7 cm c

  5. Your turn Amber: Find the length of the missing side: Green: A man starts at the village of Lymmand walks 5 km due South to Dunham. Then he walks another 8 km on a bearing of 130° to Mire. What is the direct distance between Lymmand Mire, in a straight line?

  6. Finding a missing angle • First we need to be able to rearrange the formula. a2=b2+c2-2bc cos A Rearrange to make cos A the subject of the formula a2=b2+c2-2bc cos A (+2bc cosA) a2+2bc cosA=b2+c2 (-a2) 2bc cosA=b2+c2-a2 (÷2bc) cosA=(b2+c2-a2)÷(2bc)

  7. Calculating a missing angle cos A=(62+102-92)÷(2×6×10) cos A= 0.45833333333333 A=62.720387264 A=62.7°

  8. Your turn Green: A triangle has two sides of length 30cm and an angle of 50°. Unfortunately the position of the angle is not known. Sketch two possible triangles and use them to work out the two possible lengths of the third side of the triangle. Amber: Find the missing angles.

  9. Exam Question A, B, C and D are four points on a circle.ABX and DCX are straight lines.AB = 7 cm, BX = 5 cm and CX = 6 cm. Angle BXC = 28° (a) Calculate the length of AC. Give your answer correct to 3 significant figures. (3) (b) Calculate the length of DC. (3) (Total for question = 6 marks)

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