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© John Wiley & Sons Australia, Ltd 2009 1
WorkSHEET 2 Triangle trigonometry Name: ___________________________ 1 Calculate each of the following, correct to three
decimal places. (a) tan 65° (b) sin 46° (c) cos 7°
(a) tan 65° = 2.145 (b) sin 46° = 0.719 (c) cos 7° = 0.993
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2 Find θ correct to the nearest degree, given that: (a) cos θ = 0.287 (b) tan θ = 1.873 (c) sin θ = 0.9
(a) θ = 73° (b) θ = 62° (c) θ = 64°
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3 Find the values of the unknown marked sides, correct to 2 decimal places.
cos 27° = 8x
∴ x = 8 × cos 27° x = 7.13
sin 27° = 8y
∴ y = 8 × sin 27° y = 3.63
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4 Find the value of angle θ, correct to 1 decimal place.
cos θ = 52
cos θ = 0.4 ∴ θ = 66.4°
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Maths Quest Maths B Year 11 for Queensland Chapter 4: Triangle trigonometry WorkSHEET 4.1
© John Wiley & Sons Australia, Ltd 2009 2
5 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? Give your answer correct to 2 decimal places.
sin 40° = 6h
∴ h = 6 × sin 40° h = 3.86 m (correct to 2 decimal places)
2
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.
sin θ = 5.32
sin θ = 0.5714 ∴ θ = 34.8°
2
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?
sin 70° =100h
∴ h = 100 × sin 70° h = 93.97 m So, height of kite = 93.97 m + 1.08 m So, height of kite = 95.05 m
3
Maths Quest Maths B Year 11 for Queensland Chapter 4: Triangle trigonometry WorkSHEET 4.1
© John Wiley & Sons Australia, Ltd 2009 3
8 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?
tan 10° = d60
∴ d = °10tan
60
d = 340 m (to the nearest m)
2
9 Express N40°W as a true bearing.
The bearing is (360° − 40°) = 320°T.
1
10 Express 108°T as a conventional (compass) bearing.
The compass bearing is S72°E.
1