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Maths Quest Maths B Year 11 for Queensland WorkSHEET 4.1 1 2 Chapter 4 Triangle trigonometry WorkSHEET 4.1 Triangle trigonometry Calculate each of the following correct to three decimal places. (a) tan 65° (b) sin 46° (c) cos 7° 1 Name: ___________________________ 3 (a) (b) (c) Find correct to the nearest degree, given that: (a) (a) cos = 0.287 (b) (b) tan = 1.873 (c) (c) sin = 0.9 2.145 0.719 0.993 73° 62° 64° 3 3 Find the values of unknown marked sides correct to 2 decimal places. cos 27° = 4 4 Find the value of angle correct to 1 decimal place. cos = 2 5 cos = 0.4 = 66.4° 2 x 8 x = 8 cos 27° x = 7.13 y sin 27° = 8 y = 8 sin 27° y = 3.63 Maths Quest Maths B Year 11 for Queensland 5 Chapter 4 Triangle trigonometry WorkSHEET 4.1 A ladder 6 m long rests against a vertical wall and forms an angle of 40° to the horizontal ground. How high up the wall does the ladder reach, correct to 2 decimal places? 2 2 h 6 h = 6 sin 40° h = 3.86 m (correct to 2 decimal places) sin 40° = 6 A large heavy drum is pushed 3.5 m up an inclined plane. If the inclined plane rises 2 m vertically, find the angle the inclined plane makes with the horizontal. 2 2 3 .5 sin = 0.5714 = 34.8° sin = 7 A child 1.08 m tall flies a kite with 100 m of released string which makes an angle of 70° with the horizontal. How high is the kite flying? 3 h 100 h = 100 sin 70° h = 9397 m So, height of kite = 9397 1.08 m = 95.05 m sin 70° = Maths Quest Maths B Year 11 for Queensland 8 Chapter 4 Triangle trigonometry WorkSHEET 4.1 The angle of depression of a boat from a cliff 60 m high is 10°. How far is the boat from the base of the cliff? 3 2 60 d 60 d= tan 10 d = 340 m tan 10° = 9 Express N40°W as true bearing. 1 Bearing is (360° 40°) = 320°T. 10 Express 108°T as a conventional (compass) bearing. 1 Bearing is E18°S or S72°E.