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3.04 Degrees and minutes

Worksheet
Degrees and minutes
1

Convert each angle measure into degrees and minutes, rounding your answer to the nearest minute:

a

45.5 \degree

b

123.3 \degree

c

44.75 \degree

d

116.15 \degree

e

103.07 \degree

f

15.77 \degree

g

89.379 \degree

h

202.607 \degree

i

15.5 \degree

j

170.1 \degree

k

65.75\degree

l

181.15 \degree

m

118.02 \degree

n

99.77 \degree

o

76.272 \degree

p

238.039 \degree

2

Convert each angle measure into degrees, minutes and seconds, rounding your answer to the nearest second:

a

37.07 \degree

b

31.08 \degree

c

21.36 \degree

d

24.56 \degree

e

322.932 \degree

f

339.727 \degree

g

71.4928 \degree

h

83.7727 \degree

3

Express each angle measure in terms of degrees, rounding your answer to two decimal places:

a

84 \degree 45 '

b

12 \degree 5 '

c

57 \degree 33 '

d

51\degree 45'

e

17\degree 5'

f

84 \degree 13 '

g

38 \degree 22' 12''

h

33\degree 41'24 ''

i

221 \degree 3' 36''

j

205\degree 5'24 ''

k

65 \degree 54 ' 40''

l

90\degree 43'41 ''

4

Round each angle measure to the nearest degree:

a

86 \degree 21 '

b

101\degree 6'

c

163 \degree 39 '

d

164 \degree 35'

5

Round each angle measure to the nearest minute:

a

153\degree 47' 9 ''

b

140 \degree 55' 14''

c

23\degree 33' 49 ''

d

26\degree 38'45''

6

Find the value of the following:

a

74 \degree 14 ' + 41 \degree 27 '

b

79 \degree 22 ' - 26 \degree 12 '

c

71 \degree 13 ' + 217 \degree 54 '

d

62 \degree 34 ' - 47 \degree 57 '.

e

111 \degree 18 ' - 49 \degree 46 '

f

90 \degree - 38 \degree 27 '

g

85 \degree 29' 43''- 56 \degree 13' 18''

h

90 \degree - 77 \degree 15 '45''

7

Evaluate each angle measure correct to two decimal places:

a

\cos 47 \degree 38 '

b

\sin 158 \degree 22 '

8

For each of the following, find the acute angle \theta, rounded to the nearest minute:

a

\sin \theta = 0.3168

b

\tan \theta = 2.897

c

\cos \theta = 0.8267

d

\tan \theta = 3.749

Unknown angles
9

For the following triangles, find the angle \theta to the nearest minute:

a
b
c
d
10

Consider the following triangle. Find the value of x:

a

In degrees, correct to two decimal places.

b

To the nearest minute.

11

For the following triangles, find the value of x:

i

In degrees, correct to four decimal places.

ii

To the nearest second.

a
b
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Outcomes

MS2-12-3

interprets the results of measurements and calculations and makes judgements about their reasonableness, including the degree of accuracy and the conversion of units where appropriate

MS2-12-4

analyses two-dimensional and three-dimensional models to solve practical problems

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