Introduction to trigonometry 113
from which, length of tie,
QR =
10.0 sin 39 ◦ 44
sin 120 ◦
= 7.38 m
Now try the following exercise
Exercise 51 Further problems on practical
situations involving trigonometry
1. A ship P sails at a steady speed of 45 km/h in
a direction of W 32 ◦ N (i.e. a bearing of 302 ◦ )
from a port. At the same time another ship Q
leaves the port at a steady speed of 35 km/h in
a direction N 15 ◦ E (i.e. a bearing of 015 ◦ ).
Determine their distance apart after 4 hours.
[193 km]
2. Two sides of a triangular plot of land are
52.0 m and 34.0 m, respectively. If the area
of the plot is 620 m
2 find (a) the length of
fencing required to enclose the plot and (b)
the angles of the triangular plot.
[(a) 122.6 m (b) 94 ◦ 49 , 40 ◦ 39 , 44 ◦ 32 ]
3. A jib crane is shown in Fig. 11.33. If the tie
rod PR is 8.0 long and PQ is 4.5 m long determine (a) the length of jib RQ and (b) the angle
between the jib and the tie rod.
[(a) 11.4 m (b) 17 ◦ 33 ]
130Њ
Q
R
P
Figure 11.33
4. A building site is in the form of a quadrilateral as shown in Fig. 11.34, and its area is
1510 m 2 . Determine the length of the perimeter of the site.
[163.4 m]
728
758
28.5 m
34.6 m
52.4 m
Figure 11.34
5. Determine the length of members BF and EB
in the roof truss shown in Fig. 11.35.
[B F = 3.9 m, E B = 4.0 m]
50Њ
50Њ
A
F
E
D
B
5 m
4 m
4 m
5 m
2.5 m
2.5 m
C
Figure 11.35
6. A laboratory 9.0 m wide has a span roof
which slopes at 36 ◦ on one side and 44 ◦ on
the other. Determine the lengths of the roof
slopes.
[6.35 m, 5.37 m]
11.12 Further practical situations
involving trigonometry
Problem 34. A vertical aerial stands on
horizontal ground. A surveyor positioned due east
of the aerial measures the elevation of the top as
48 ◦ . He moves due south 30.0 m and measures the
elevation as 44 ◦ . Determine the height of the aerial.
In Fig. 11.36, DC represents the aerial, A is the initial
position of the surveyor and B his final position.
From triangle ACD, tan 48
◦
=
DC
AC
,
from which
AC =
DC
tan 48 ◦
Similarly, from triangle BCD,
BC =
DC
tan 44 ◦
from which, length of tie,
QR =
10.0 sin 39 ◦ 44
sin 120 ◦
= 7.38 m
Now try the following exercise
Exercise 51 Further problems on practical
situations involving trigonometry
1. A ship P sails at a steady speed of 45 km/h in
a direction of W 32 ◦ N (i.e. a bearing of 302 ◦ )
from a port. At the same time another ship Q
leaves the port at a steady speed of 35 km/h in
a direction N 15 ◦ E (i.e. a bearing of 015 ◦ ).
Determine their distance apart after 4 hours.
[193 km]
2. Two sides of a triangular plot of land are
52.0 m and 34.0 m, respectively. If the area
of the plot is 620 m
2 find (a) the length of
fencing required to enclose the plot and (b)
the angles of the triangular plot.
[(a) 122.6 m (b) 94 ◦ 49 , 40 ◦ 39 , 44 ◦ 32 ]
3. A jib crane is shown in Fig. 11.33. If the tie
rod PR is 8.0 long and PQ is 4.5 m long determine (a) the length of jib RQ and (b) the angle
between the jib and the tie rod.
[(a) 11.4 m (b) 17 ◦ 33 ]
130Њ
Q
R
P
Figure 11.33
4. A building site is in the form of a quadrilateral as shown in Fig. 11.34, and its area is
1510 m 2 . Determine the length of the perimeter of the site.
[163.4 m]
728
758
28.5 m
34.6 m
52.4 m
Figure 11.34
5. Determine the length of members BF and EB
in the roof truss shown in Fig. 11.35.
[B F = 3.9 m, E B = 4.0 m]
50Њ
50Њ
A
F
E
D
B
5 m
4 m
4 m
5 m
2.5 m
2.5 m
C
Figure 11.35
6. A laboratory 9.0 m wide has a span roof
which slopes at 36 ◦ on one side and 44 ◦ on
the other. Determine the lengths of the roof
slopes.
[6.35 m, 5.37 m]
11.12 Further practical situations
involving trigonometry
Problem 34. A vertical aerial stands on
horizontal ground. A surveyor positioned due east
of the aerial measures the elevation of the top as
48 ◦ . He moves due south 30.0 m and measures the
elevation as 44 ◦ . Determine the height of the aerial.
In Fig. 11.36, DC represents the aerial, A is the initial
position of the surveyor and B his final position.
From triangle ACD, tan 48
◦
=
DC
AC
,
from which
AC =
DC
tan 48 ◦
Similarly, from triangle BCD,
BC =
DC
tan 44 ◦