Higher Engineering Mathematics, Sixth Edition

Introduction to trigonometry 115

AngleOA′B′= 180 ◦− 120 ◦− 16 ◦ 47 ′= 43 ◦ 13 ′.

Applying the sine rule:

30. 0

sin120◦

=

OB′

sin43◦ 13 ′

from which,

OB′=

30 .0sin43◦ 13 ′

sin120◦

= 23 .72cm

SinceOB= 35 .43cm andOB′= 23 .72cm thenBB′=
35. 43 − 23. 72 = 11 .71cm.

HenceBmoves 11.71cm when angleAOBchanges
from 50◦to 120◦.

Problem 36. The area of a field is in the form of a

quadrilateralABCDas shown in Fig. 11.39.

Determine its area.

62.3 m

21.4 m

39.8 m

568

1148

D

A

B

C

42.5 m

Figure 11.39

A diagonal drawn fromBtoDdivides the quadrilateral
into two triangles.

Area of quadrilateral ABCD

=area of triangleABD+area of triangleBCD

=^12 ( 39. 8 )( 21. 4 )sin114◦+^12 ( 42. 5 )( 62. 3 )sin 56◦

= 389. 04 + 1097. 5 =1487m^2

Now try the following exercise

Exercise 52 Further problemson practical

situations involving trigonometry

1. PQandQRare the phasors representing the
   alternating currents in two branches of a cir-
   cuit. PhasorPQis 20.0A and is horizontal.

PhasorQR(which is joined to the end ofPQ

to form trianglePQR) is 14.0A and is at an

angle of 35◦to the horizontal. Determine the

resultant phasorPRand theangleit makes with

phasorPQ. [32.48A, 14◦ 19 ′]

2. Three forces acting on a fixed point are repre-
   sented by the sides of a triangle of dimensions
   7.2cm, 9.6cm and 11.0cm. Determine the
   angles between the lines of action and the
   three forces. [80◦ 25 ′, 59 ◦ 23 ′, 40 ◦ 12 ′]


3. Calculate, correct to 3 significant figures, the
   co-ordinatesxandyto locate the hole centre
   atPshown in Fig. 11.40.
   [x=69.3mm,y=142mm]

x 100 mm

P

y

116 ^140 

Figure 11.40

4. An idler gear, 30mm in diameter, has to be
   fitted between a 70mm diameter driving gear
   and a 90mm diameter driven gear as shown
   in Fig. 11.41. Determine the value of angleθ
   between the center lines. [130◦]

70 mm dia

30 mm dia

90 mm dia

99.78 mm

Figure 11.41

5. A reciprocating engine mechanism is shown
   in Fig. 11.42. The crankABis 12.0cm long
   and the connecting rodBCis 32.0cm long.