Basic Engineering Mathematics, Fifth Edition

180 Basic Engineering Mathematics

B AX A^9

Q

C

P S

Z

U

V

R

Y

Figure 20.50

With reference to Figure 20.50:

(i) Draw a straight line 5cm long and label itXY.

(ii) ProduceXYany distancetoB. With compass cen-

tred atXmake an arc atAandA′. (The lengthXA

andXA′is arbitrary.) With compass centred atA

draw the arcPQ. With the same compass setting

and centred atA′,drawthearcRS. Join the inter-

section of the arcs,CtoX, and a right angle to

XYis produced atX. (Alternatively, a protractor

can be used to construct a 90◦angle.)

(iii) Thehypotenuseisalwaysoppositetherightangle.

Thus, YZ is opposite ∠X. Using a compass

centred atY and set to 6.5cm, describe the

arcUV.

(iv) The intersectionof the arcUVwithXCproduced,

forms the vertexZof the required triangle. Join

YZwith a straight line.

Now try the following Practice Exercise

PracticeExercise 81 Construction of

triangles (answers on page 349)

In the following, construct the trianglesABCfor

the given sides/angles.

1. a=8cm,b=6cm andc=5cm.


2. a=40mm,b=60mm andC= 60 ◦.


3. a=6cm,C= 45 ◦andB= 75 ◦.


4. c=4cm,A= 130 ◦andC= 15 ◦.


5. a=90mm,B= 90 ◦,hypotenuse=105mm.