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
UNIT 6 – TRIGONOMETRY OF RIGHT TRIANGLES Lesson 6 – Sine and Cosine Ratios Labelling – Label the sides of each triangle. A θ θ B C Sine Ratio – the ratio of the opposite side to the hypotenuse 𝑠𝑖𝑛 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 Cosine Ratio – the ratio of the adjacent side to the hypotenuse 𝑐𝑜𝑠 𝜃 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 From ∠𝐴 From ∠𝐶 sin A = sin C = 3 cm cos A = cos C = B A 5 cm C 4 cm Mneumonic: S O H 𝑠𝑖𝑛 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 C A H , 𝑐𝑜𝑠 𝜃 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 T O A , 𝑡𝑎𝑛 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 D) Examples Example 1: Determine sin A and cos A, correct to the nearest thousandth. B C 5 cm 10 cm A Example 2: Evaluate to the nearest thousandth. a) sin 54° b) sin 19° c) cos 89° d) cos 6° Example 3: Calculate ∠𝐴, to the nearest degree. a) sin A = 1 3 b) sin A = 0.631 c) cos A = 0.217 d) cos A = 0.217 Applications of Sine and Cosine Ratios Example 4: A rope attached to a kite is 10 m long. The boy holding the rope estimates that the angle between the rope and the ground (angle of elevation) is 35°. Calculate the height of the kite. Example 5: A ladder leaning against a wall makes an angle of 53° with the ground (angle of elevation). If the foot of the ladder is 1.5 m from the wall, calculate the length of the ladder. Example 6: Solve the triangle. NOTE: To solve the triangle means to find all the unknown sides and all the unknown angles. a) b) A A B 61° 23 cm 9 cm B 18 cm C C