Chapter 11

Introduction to trigonometry

11.1 Trigonometry

Trigonometryisthebranchofmathematicswhichdeals
with the measurement of sides and angles of trian-
gles, and their relationship with each other. There are
many applications in engineering where a knowledge
of trigonometry is needed.

11.2 The theorem of Pythagoras

With reference to Fig. 11.1, the side opposite the right
angle(i.e.sideb)iscalledthehypotenuse.Thetheorem
of Pythagorasstates:
‘In any right-angled triangle, the square on the
hypotenuse is equal to the sum of the squares on the
other two sides.’
Hence b^2 =a^2 +c^2

B

A

a C

b

c

Figure 11.1

Problem 1. In Fig. 11.2, find the length ofEF.

E d F

D

f 5 5cm

e 5 13cm

Figure 11.2

By Pythagoras’ theorem:

e^2 =d^2 +f^2

Hence 132 =d^2 + 52

169 =d^2 + 25

d^2 = 169 − 25 = 144

Thus d=

√

144 =12cm

i.e. EF=12cm

Problem 2. Two aircraft leave an airfield at the

same time. One travels due north at an average

speed of 300km/h and the other due west at an

average speed of 220km/h. Calculate their distance

apart after 4hours.

After 4hours, the first aircraft has travelled 4× 300 =

1200km, due north, and the second aircraft has trav-

elled 4× 220 =880km due west, as shown in Fig. 11.3.

Distance apart after 4hours=BC.

A

N B

W E

S

C

1200km

880km

Figure 11.3

From Pythagoras’ theorem:

BC^2 = 12002 + 8802 = 1440000 + 774400

andBC=

√

( 2214400 )

Hence distance apart after 4 hours=1488km.