Introduction to trigonometry 187
Problem 16. In triangle EFG in Figure 21.16,
calculate angle G
E
F
G
2.30 cm
8. 71 cm
Figure 21.16
With reference to ∠G, the two sides of the triangle given
are the opposite side EF and the hypotenuse EG; hence,
sine is used,
i.e.
sin G =
2.30
8.71
= 0.26406429 ...
from which,
G = sin
−1 0.26406429 ...
i.e.
G = 15.311360
◦
Hence,
∠G = 15.31
◦ or 15
◦ 19
.
Problem 17. Evaluate the following expression,
correct to 3 significant figures
4.2 tan 49 ◦ 26 − 3.7 sin 66 ◦ 1
7.1 cos 29 ◦ 34
By calculator:
tan 49
◦ 26
= tan
49
26
60
◦
= 1.1681,
sin 66
◦ 1
= 0.9137 and cos 29
◦ 34
= 0.8698
Hence, 4.2 tan 49 ◦ 26 − 3.7 sin66 ◦ 1
7.1 cos29 ◦ 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
Practice Exercise 84 Evaluating
trigonometric ratios (answers on page 349)
1. Determine, correct to 4 decimal places,
3 sin66 ◦ 41 .
2. Determine, correct to 3 decimal places,
5 cos14
◦ 15
.
3. Determine, correct to 4 significant figures,
7 tan79 ◦ 9 .
4. Determine
(a) sine
2π
3
(b) cos 1.681 (c) tan 3.672
5. Find the acute angle sin −1 0.6734 in degrees,
correct to 2 decimal places.
6. Find the acute angle cos −1 0.9648 in degrees,
correct to 2 decimal places.
7. Find the acute angle tan −1 3.4385 in degrees,
correct to 2 decimal places.
8. Find the acute angle sin
−1 0.1381 in degrees
and minutes.
9. Find the acute angle cos −1 0.8539 in degrees
and minutes.
10. Find the acute angle tan −1 0.8971 in degrees
and minutes.
11. In the triangle shown in Figure 21.17, determine angle θ, correct to 2 decimal places.
5
9
Figure 21.17
12. In the triangle shown in Figure 21.18, determine angle θ in degrees and minutes.
8
23
Figure 21.18
Problem 16. In triangle EFG in Figure 21.16,
calculate angle G
E
F
G
2.30 cm
8. 71 cm
Figure 21.16
With reference to ∠G, the two sides of the triangle given
are the opposite side EF and the hypotenuse EG; hence,
sine is used,
i.e.
sin G =
2.30
8.71
= 0.26406429 ...
from which,
G = sin
−1 0.26406429 ...
i.e.
G = 15.311360
◦
Hence,
∠G = 15.31
◦ or 15
◦ 19
.
Problem 17. Evaluate the following expression,
correct to 3 significant figures
4.2 tan 49 ◦ 26 − 3.7 sin 66 ◦ 1
7.1 cos 29 ◦ 34
By calculator:
tan 49
◦ 26
= tan
49
26
60
◦
= 1.1681,
sin 66
◦ 1
= 0.9137 and cos 29
◦ 34
= 0.8698
Hence, 4.2 tan 49 ◦ 26 − 3.7 sin66 ◦ 1
7.1 cos29 ◦ 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
Practice Exercise 84 Evaluating
trigonometric ratios (answers on page 349)
1. Determine, correct to 4 decimal places,
3 sin66 ◦ 41 .
2. Determine, correct to 3 decimal places,
5 cos14
◦ 15
.
3. Determine, correct to 4 significant figures,
7 tan79 ◦ 9 .
4. Determine
(a) sine
2π
3
(b) cos 1.681 (c) tan 3.672
5. Find the acute angle sin −1 0.6734 in degrees,
correct to 2 decimal places.
6. Find the acute angle cos −1 0.9648 in degrees,
correct to 2 decimal places.
7. Find the acute angle tan −1 3.4385 in degrees,
correct to 2 decimal places.
8. Find the acute angle sin
−1 0.1381 in degrees
and minutes.
9. Find the acute angle cos −1 0.8539 in degrees
and minutes.
10. Find the acute angle tan −1 0.8971 in degrees
and minutes.
11. In the triangle shown in Figure 21.17, determine angle θ, correct to 2 decimal places.
5
9
Figure 21.17
12. In the triangle shown in Figure 21.18, determine angle θ in degrees and minutes.
8
23
Figure 21.18