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MEP: Demonstration Project Teacher Support Y9B UNIT 15 Trigonometry Extra Exercises 15.1 Give all answers to 3 significant figures, unless otherwise stated. 1. Calculate the length of the unknown side in each of the following triangles: (a) (b) 8 cm 17 cm 11 cm 14 cm (c) (d) 9 cm 16 cm 20 m 5m 2. A rectangle has sides of length 14 cm and 7 cm. Calculate the length of a diagonal of the rectangle. 3. A ship sails 100 km north and then 200 km east. How far is the ship from its starting point? 4. Calculate the area and perimeter of this trapezium: 8 cm 6 cm 4 cm 5. A square has a diagonal of length 40 cm. Determine the length of the sides of the square. © The Gatsby Charitable Foundation 5 cm MEP: Demonstration Project Teacher Support Y9B UNIT 15 Trigonometry 1. Extra Exercises 15.2 Calculate sin θ for each of the following triangles. Comment on the values you obtain. (a) (b) 2 cm 14 cm 1 cm 3. 142 cm 7 cm 71 cm θ θ 2. (c) θ Use your calculator to determine the following, correct to 4 decimal places: (a) sin 72 ° (b) tan 33 ° (c) cos 3.6 ° (d) sin 13.9 ° (e) tan 24.7 ° (f) cos 45 ° Use your calculator to determine θ , correct to 1 decimal place, if: (a) sin θ = 0.7 (b) cosθ = 0.4 (c) tan θ = 14 (d) cosθ = 0.6 (e) sin θ = 0.9 (f) tan θ = 0.1 © The Gatsby Charitable Foundation MEP: Demonstration Project Teacher Support Y9B UNIT 15 Trigonometry Extra Exercises 15.3 Give all answers to 3 significant figures, unless otherwise stated. 1. Calculate the lengths of the sides marked with letters in each of the following diagrams: b (a) (b) 44 cm y a 14 cm 28˚ x 62˚ 8 cm (c) (d) 52˚ 25˚ 15 m h a 2. A rectangle has sides of length 18 cm and x cm . The acute angle between the diagonals of the rectangle is 40 ° . Determine x . 3. A pole of length 6 m leans against a vertical wall. The angle between the pole and the horizontal is 70 ° . Calculate the height of the top of the pole. 4. Determine the length of the base of the triangle shown. 50˚ 8 cm © The Gatsby Charitable Foundation 8 cm MEP: Demonstration Project Teacher Support Y9B UNIT 15 Trigonometry 1. Extra Exercises 15.4 Calculate the size of the angle θ , marked in each triangle. Also calculate the length of the unknown side of each triangle. Give your answers to 3 significant figures. (a) (b) 12 cm 15 cm θ 40 cm θ 8 cm (c) 15 cm (d) 8m 12 cm θ θ 20 m A 2. In the diagram shown, calculate the angles α and β if the diagonal BD has length 10 cm. Give your answers to 1 decimal place. 8 cm 8 cm D α B 12 cm 12 cm β 3. A right angled triangle has sides of length 5 m, 12 m and 13 m. C Calculate, to 1 decimal place, the sizes of the angles of this triangle. 4. An isosceles triangle has sides of length 8 cm, 8 cm and 6 cm. Determine the sizes of the angles in this triangle, to 2 significant figures. 5. Calculate the size of the acute angle between the two diagonals of a rectangle which has sides of length 8 cm and 12 cm. Give your answer to 3 significant figures. © The Gatsby Charitable Foundation MEP: Demonstration Project Teacher Support Y9B Extra Exercises 15.1 Answers 1. (a) 16.1 cm 2. 15.7 cm 3. 224 km 4. 46.9 cm 2 , 5. 28.3 cm (b) 20.2 cm (c) 19.4 cm (d) 13.2 cm 34.5 cm Extra Exercises 15.2 Answers 1. (a) 0.5 (b) 0.5 (c) 0.5 Always the same because θ is the same angle. 2. (a) (d) 0.9511 0.2402 (b) (e) 0.6494 0.4599 (c) (f) 0.9980 0.7071 3. (a) 44.4 ° (b) 66.4 ° (c) 85.9 ° (d) 53.1 ° (e) 64.2 ° (f) 5.7 ° (b) a = 6.6 cm, Extra Exercises 15.3 Answers 1. (a) x = 38.8 cm, (c) h = 13.0 cm 2. 6.55 cm 3. 5.64 m 4. 6.76 cm y = 20.7 cm (d) b = 12.4 cm a = 35.5 cm Extra Exercises 15.4 Answers Angle θ : (a) 57.8 ° (b) 16.7 ° (c) 51.3 ° (d) 23.6 ° Side length: (a) 12.7 cm (b) 41.8 cm (c) 19.2 cm (d) 18.3 cm 2. α = 116.7 ° , β = 49.2 ° 3. 67.4 °, 4. 44 °, 5. 67.4 ° 1. 22.6 °, 68 °, 90 ° 68 ° © The Gatsby Charitable Foundation