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TRIGONOMETRY REVISION NAME__________________________ (2) Question 3 Use your calculator to find, correct to four decimal places: (a) tan 62 Identify the sides and trigonometric ratio to use Question 1 (2) (b) sin 1548 (a) (2) Question 4 (a) Convert 9.68 to degrees and minutes. (b) (b) Convert 2315 to decimal degrees. Section A: Measurement, chance and data 5.5 (2) Question 2 Which trigonometric ratio should be used to find the value of the pronumeral in each of the following diagrams? (a) (2) Question 5 Find the value of the pronumeral in the triangle below, where tan = 4. d 12 19.7 m 78 x (b) 15 cm 12 cm (2) Find the value of the pronumeral in this diagram. Question 6 (1) A kite is attached to a string 22 m long. If the string makes an angle of 42.6° to the horizontal, what is the height of the kite? Question 9 26 cm h 37 (2) Find the equivalent first quadrant trigonometric ratio for: (a) sin115 Question 7 Question 10 (6) A makeshift ramp is rested on a stack of bricks as in the diagram. 0.6 m (b) cos 330 r h 18 (2) Question 7 Find the value of the pronumeral in this diagram. 1.4 m If the ramp protrudes 0.6 m beyond the top of the bricks: (a) find the total length of the ramp 16.2 m k 24 Question 8 (1) Convert the conventional bearing S35E to true bearing. (b) find the height of the bricks (c) find how far above the bricks the ramp protrudes. (2) The angle of elevation of the top of a building from a point on the ground 150 m away is 67. Calculate the height of the building correct to the nearest metre. Question 11 (6) The diagram below shows two angles of elevation (35° and 65°) of the top of a tower. The points from which the angles are measured are 20 m apart. Question 14 h 65 b 35 20 m (a) Write an equation involving the smaller angle and h and b. Transpose it so that b is the subject. Section C: Measurement, chance and data 6.0 Question 12 (b) Write an equation involving the larger angle and h and b. Transpose it so that b is the subject. (3) The angle of depression from the top of a 120 m cliff to a boat out at sea is 2815. Find the direct distance between the boat and the top of the cliff, correct to two decimal places. (c) Equate the two equations above to find the height of the tower. Question 13 (1) Choose the correct answer. The angle of elevation of the top of a tree from a point on the ground 12 m away is 52. What is the height of the tree is closest to: (d) Find the horizontal distances from the base of the tower, correct to the nearest metre. Question 15 A cylindrical piece of hollow pipe is 35 cm long and has both ends covered with plastic. A tiny hole is made in the middle of one end and a piece of wire is threaded through. The wire does not bend. If the pipe has a diameter of 15 cm, find: (a) the angle the wire makes with the plastic if it touches the opposite end where the plastic meets the pipe (b) the length of wire within the pipe. 35 cm (c) What is the angle the wire makes with the length of the cylinder. Section D: Beyond 6.0 Question 16 A boat starts at A and sails 6 km on a bearing of 130° True to point B and then turns and sails on a bearing of 200° True for another 10 km to C. (a) How far south of A is C correct to the nearest tenth of a kilometre? (draw the diagram first) (b) What is the bearing, correct to the nearest degree, of C from A in True Bearing?