Angles and triangles 167
(i) 47 + 34 = 81
(ii) Since 60 = 1 , 81 = 1 21
(iii) The 21 is placed in the seconds column and 1
is carried in the minutes column.
(iv) 51 + 27 + 1 = 79
(v) Since 60 = 1 ◦ , 79 = 1 ◦ 19
(vi) The 19 is placed in the minutes column and 1 ◦
is carried in the degrees column.
(vii) 19 ◦ + 63 ◦ + 1 ◦ (carried) = 83 ◦ . Place 83 ◦ in the
degrees column.
This answer can be obtained using the calculator as
follows.
1. Enter 19
2. Press
◦ ’ ’ ’
3. Enter 51
4. Press ◦ ’ ’ ’
5. Enter 47
6. Press ◦ ’ ’ ’
7. Press +
8. Enter 63
9. Press ◦ ’ ’ ’
10. Enter 27
11. Press ◦ ’ ’ ’
12. Enter 34
13. Press ◦ ’ ’ ’
14. Press =
Answer = 83
◦ 19 21
Thus, 19
◦ 51 47 + 63
◦ 27 34 = 83
◦ 19 21 .
Problem 4. Convert 39 ◦ 27 to degrees in decimal
form
39
◦ 27
= 39
27 ◦
60
27 ◦
60
= 0.45
◦ by calculator
Hence,
39
◦ 27
= 39
27 ◦
60
= 39.45
◦
This answer can be obtained using the calculator as
follows.
1. Enter 39
2. Press ◦ ’ ’ ’
3. Enter 27
4. Press ◦ ’ ’ ’
5. Press =
6. Press ◦ ’ ’ ’
Answer = 39.45
◦
Problem 5. Convert 63 ◦ 26 51 to degrees in
decimal form, correct to 3 decimal places
63
◦ 26
51
= 63
◦ 26
51
60
= 63
◦ 26.85
63
◦ 26.85
= 63
26.85 ◦
60
= 63.4475
◦
Hence, 63
◦ 26
51
= 63.448
◦ correct to 3 decimal
places.
This answer can be obtained using the calculator as
follows.
1. Enter 63
2. Press ◦ ’ ’ ’ 3. Enter 26
4. Press ◦ ’ ’ ’ 5. Enter 51
6. Press ◦ ’ ’ ’
7. Press =
8. Press ◦ ’ ’ ’ Answer = 63.4475
◦
Problem 6. Convert 53.753 ◦ to degrees, minutes
and seconds
0.753
◦
= 0.753 × 60
= 45.18
0.18
= 0.18 × 60
= 11
to the nearest second
Hence, 53.753
◦
= 53
◦ 45
11
This answer can be obtained using the calculator as
follows.
1. Enter 53.753
2. Press =
3. Press ◦ ’ ’ ’
Answer = 53
◦ 45 10.8
Now try the following Practice Exercise
Practice Exercise 76 Angular measurement
(answers on page 348)
1. Evaluate 52 ◦ 39 + 29 ◦ 48
2. Evaluate 76 ◦ 31 − 48 ◦ 37
3. Evaluate 77 ◦ 22 + 41 ◦ 36 − 67 ◦ 47
4. Evaluate 41 ◦ 37 16 + 58 ◦ 29 36
5. Evaluate 54 ◦ 37 42 − 38 ◦ 53 25
6. Evaluate 79 ◦ 26 19 − 45 ◦ 58 56 + 53 ◦ 21 38
7. Convert 72 ◦ 33 to degrees in decimal form.
8. Convert 27 ◦ 45 15 to degrees correct to 3
decimal places.
9. Convert 37.952 ◦ to degrees and minutes.
10. Convert 58.381 ◦ to degrees, minutes and
seconds.
Here are some further worked examples on angular
measurement.
Problem 7. State the general name given to the
following angles: (a) 157 ◦ (b) 49 ◦ (c) 90 ◦ (d) 245 ◦
(a) Any angle between 90 ◦ and 180 ◦ is called an
obtuse angle.
Thus, 157 ◦ is an obtuse angle.
(b) Any angle between 0 ◦ and 90 ◦ is called an acute
angle.