Basic Engineering Mathematics, Fifth Edition

182 Basic Engineering Mathematics

PQRis a 3, 4, 5 triangle. There are not many right-

angled triangles which have integer values (i.e. whole

numbers) for all three sides.

Problem 2. In Figure 21.3, find the length ofEF

E d F

D

f 5 5cm e^5 13cm

Figure 21.3

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. d=EF=12cm

DEF is a 5, 12, 13 triangle, another right-angled

triangle which has integer values for all three sides.

Problem 3. 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 4 hours, the first aircraft has travelled

4 × 300 =1200km due north

and the second aircraft has travelled

4 × 220 =880km due west,

as shown in Figure 21.4. The distance apart after

4hours=BC.

A

N B

W E

S

C

1200km

880km

Figure 21.4

From Pythagoras’ theorem,

BC^2 = 12002 + 8802

= 1440000 + 774400 = 2214400

and BC=

√

2214400 =1488km.

Hence, distance apart after 4 hours=1488km.

Now try the following Practice Exercise

PracticeExercise 82 Theorem of

Pythagoras (answers on page 350)

1. Find the length of sidexin Figure 21.5.

41cm

40cm

x

Figure 21.5

2. Find the length of sidexin Figure 21.6(a).


3. Find the length of sidexin Figure 21.6(b),
   correct to 3 significant figures.

25m

(a)

7m

4.7mm

8.3mm

(b)

x

x

Figure 21.6

4. In a triangleABC,AB=17cm,BC=12cm
   and∠ABC= 90 ◦. Determine the length of
   AC, correct to 2 decimal places.


5. A tent peg is 4.0m away from a 6.0m high
   tent. What length of rope, correct to the