Basic Engineering Mathematics, Fifth Edition

Introduction to trigonometry 187

Problem 16. In triangleEFGin Figure 21.16,

calculate angleG

E

F G

2.30cm

8.71cm

Figure 21.16

Withreference to∠G, the twosides of the trianglegiven
are the oppositesideEFand the hypotenuseEG; hence,
sine is used,

i.e. sinG=

2. 30

8. 71

= 0. 26406429 ...

from which, G=sin−^10. 26406429 ...

i.e. G= 15. 311360 ◦

Hence, ∠G= 15. 31 ◦or 15 ◦ 19 ′.

Problem 17. Evaluate the following expression,

correct to 3 significant figures

4 .2tan49◦ 26 ′− 3 .7sin66◦ 1 ′

7 .1cos29◦ 34 ′

By calculator:

tan49◦ 26 ′=tan

(

49

26

60

)◦

= 1. 1681 ,

sin66◦ 1 ′= 0 .9137 and cos29◦ 34 ′= 0. 8698

Hence,^4 .2tan49
◦ 26 ′− 3 .7sin66◦ 1 ′
7 .1cos29◦ 34 ′

=

( 4. 2 × 1. 1681 )−( 3. 7 × 0. 9137 )

( 7. 1 × 0. 8698 )

=

4. 9060 − 3. 3807

6. 1756

=

1. 5253

6. 1756

= 0. 2470 =0.247,

correct to 3 significant figures.

Now try the following Practice Exercise

PracticeExercise 84 Evaluating

trigonometric ratios (answers on page 349)

1. Determine, correct to 4 decimal places,
   3sin66◦ 41 ′.
   2. Determine, correct to 3 decimal places,
   5cos14◦ 15 ′.
   3. Determine, correct to 4 significant figures,
   7tan79◦ 9 ′.
   4. Determine

(a) sine

2 π

3

(b) cos1.681 (c) tan3. 672

5. Find the acute angle sin−^10 .6734 in degrees,
   correct to 2 decimal places.


6. Findthe acute angle cos−^10 .9648 indegrees,
   correct to 2 decimal places.


7. Find the acute angle tan−^13 .4385 in degrees,
   correct to 2 decimal places.


8. Find the acute angle sin−^10 .1381 in degrees
   and minutes.


9. Find the acute angle cos−^10 .8539 in degrees
   and minutes.


10. Find the acute angle tan−^10 .8971 in degrees
    and minutes.


11. In the triangle shown in Figure 21.17, deter-
    mine angleθ, correct to 2 decimal places.



5

9

Figure 21.17

12. In the triangle shown in Figure 21.18, deter-
    mine angleθin degrees and minutes.



8

23

Figure 21.18