Download Worksheet 4.1

Maths Quest Maths B Year 11 for Queensland
WorkSHEET 4.1
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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°
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Name: ___________________________
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(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°
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Find the values of unknown marked sides
correct to 2 decimal places.
cos 27° =
4
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Find the value of angle  correct to 1 decimal
place.
cos  =
2
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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
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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.
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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 = 9397 m
So, height of kite = 9397  1.08 m = 95.05 m
sin 70° =
Maths Quest Maths B Year 11 for Queensland
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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?
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2
60
d
60
d=
tan 10
d = 340 m
tan 10° =
9
Express N40°W as true bearing.
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Bearing is (360°  40°) = 320°T.
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Express 108°T as a conventional (compass)
bearing.
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Bearing is E18°S or S72°E.