Basic Engineering Mathematics, Fifth Edition

Angles and triangles 179

20.6 Construction of triangles

To construct any triangle, the followingdrawing instru-
ments are needed:

(a) ruler and/or straight edge

(b) compass

(c) protractor

(d) pencil.

Here are some worked problems todemonstrate triangle
construction.

Problem 30. Construct a triangle whose sides are

6cm,5cmand3cm

D

F

E

C G

A 6cm B

Figure 20.47

With reference to Figure 20.47:

(i) Draw a straight line of any length and, with a pair

of compasses, mark out 6cm length and label it

AB.

(ii) Set compass to5cm and withcentre atAdescribe

arcDE.

(iii) Set compass to 3cm and withcentre atBdescribe

arcFG.

(iv) The intersection of the two curves atCis the ver-

tex of the required triangle. JoinACandBCby

straight lines.

It may be proved by measurement that the ratio of the
angles of a triangle is not equal to the ratio of the sides
(i.e., in this problem, the angle opposite the 3cm side is
not equal to half the angle opposite the 6cm side).

Problem 31. Construct a triangleABCsuch that

a=6cm,b=3cm and∠C= 60 ◦

With reference to Figure 20.48:

C

A

B a 5 6cm

608

b 5 3cm

Figure 20.48

(i) Draw a lineBC,6cm long.

(ii) Using a protractor centred atC,makeanangleof

60 ◦toBC.

(iii) FromCmeasure a length of 3cm and labelA.

(iv) JoinBtoAby a straight line.

Problem 32. Construct a trianglePQRgiven that

QR=5cm,∠Q= 70 ◦and∠R= 44 ◦

QR

P

Q 9

R 9

(^708448)
5cm
Figure 20.49
With reference to Figure 20.49:
(i) Draw a straight line 5cm long and label itQR.
(ii) Use a protractor centred atQand make an angle
of 70◦.DrawQQ′.
(iii) Use a protractor centred atRand make an angle
of 44◦.DrawRR′.
(iv) The intersection ofQQ′andRR′forms the vertex
Pof the triangle.
Problem 33. Construct a triangleXYZgiven that
XY=5cm, the hypotenuseYZ= 6 .5cm and
∠X= 90 ◦