Basic Engineering Mathematics, Fifth Edition

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 thecalculatoras
follows.

1. Enter 19 2. Press◦’ ’ ’ 3. Enter 51


2. Press◦’’’ 5. Enter47 6. Press◦’’’


3. Press+ 8. Enter 63 9. Press◦’’’


4. Enter 27 11. Press◦’’’


5. Enter 34 13. Press◦’’’


6. 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 thecalculatoras
follows.

1. Enter 39 2. Press◦’’’ 3. Enter27


2. 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 thecalculatoras
follows.

1. Enter 63 2. Press◦’’’ 3. Enter26


2. Press◦’’’ 5. Enter51 6. Press◦’’’


3. 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 thecalculatoras

follows.

1. Enter 53.753 2. Press=


2. Press◦’’’ Answer= 53 ◦ 45 ′ 10. 8 ′′

Now try the following Practice Exercise

PracticeExercise 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. Evaluate79◦ 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.