Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
+ The Cosine Rule Monday 6th 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 to the length opposite. c A a b C + Trigonometry in Real Life https://www.youtube.com/watch?v=WehHFJki9yQ + The cosine Rule a2=b2+c2-2bc cos A We use this formula to calculate a missing length in a triangle. C b 13 cm Firstly label your triangle. a x 76° A 7 cm c B Then you need to substitute the values into the formula: a2= 132+72 – 2×13×7×cos76 Now you need your calculator. Make sure it is in degree mode! a2= 67.9716977384 a= 8.24449499596 a=8.24cm + Your turn Amber: Green: Find the length of the missing side: A man starts at the village of Lymm and 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 Lymm and Mire, in a straight line? + 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) + Calculating a missing angle cos A=(62+102-92)÷(2×6×10) cos A= 0.45833333333333 A=62.720387264 A=62.7° + Your turn Amber: Green: Find the missing angles. 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. + 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)