180 Basic Engineering Mathematics
A9
B
A
X
Q
C
P
S
Z
U
V
R
Y
Figure 20.50
With reference to Figure 20.50:
(i) Draw a straight line 5 cm long and label it XY.
(ii) Produce XY any distance to B. With compass centred at X make an arc at A and A . (The length XA
and XA is arbitrary.) With compass centred at A
draw the arc PQ. With the same compass setting
and centred at A , draw the arc RS. Join the intersection of the arcs, C to X , and a right angle to
XY is produced at X . (Alternatively, a protractor
can be used to construct a 90 ◦ angle.)
(iii) The hypotenuse is always opposite the right angle.
Thus, YZ is opposite ∠X . Using a compass
centred at Y and set to 6.5 cm, describe the
arc UV.
(iv) The intersection of the arc UV with XC produced,
forms the vertex Z of the required triangle. Join
YZ with a straight line.
Now try the following Practice Exercise
Practice Exercise 81 Construction of
triangles (answers on page 349)
In the following, construct the triangles ABC for
the given sides/angles.
1. a = 8 cm, b = 6 cm and c = 5 cm.
2. a = 40 mm, b = 60 mm and C = 60 ◦ .
3. a = 6 cm, C = 45 ◦ and B = 75 ◦ .
4. c = 4 cm, A = 130 ◦ and C = 15 ◦ .
5. a = 90 mm, B = 90 ◦ , hypotenuse = 105mm.