WorkSHEET 2 Triangle trigonometry Name: - The … · WorkSHEET 2 Triangle trigonometry Name: ... 5...

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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 3 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° 3 3 Find the values of the unknown marked sides, correct to 2 decimal places. cos 27° = 8 x x = 8 × cos 27° x = 7.13 sin 27° = 8 y y = 8 × sin 27° y = 3.63 4 4 Find the value of angle θ, correct to 1 decimal place. cos θ = 5 2 cos θ = 0.4 θ = 66.4° 2

Transcript of WorkSHEET 2 Triangle trigonometry Name: - The … · WorkSHEET 2 Triangle trigonometry Name: ... 5...

Page 1: WorkSHEET 2 Triangle trigonometry Name: - The … · WorkSHEET 2 Triangle trigonometry Name: ... 5 A ladder 6 m long rests against a vertical wall ... 10 Express 108°T as a conventional

© 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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Page 2: WorkSHEET 2 Triangle trigonometry Name: - The … · WorkSHEET 2 Triangle trigonometry Name: ... 5 A ladder 6 m long rests against a vertical wall ... 10 Express 108°T as a conventional

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)

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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°

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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

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Page 3: WorkSHEET 2 Triangle trigonometry Name: - The … · WorkSHEET 2 Triangle trigonometry Name: ... 5 A ladder 6 m long rests against a vertical wall ... 10 Express 108°T as a conventional

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)

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9 Express N40°W as a true bearing.

The bearing is (360° − 40°) = 320°T.

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10 Express 108°T as a conventional (compass) bearing.

The compass bearing is S72°E.

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