140
Basic Engineering Mathematics
V Z P U
A b ⫽ 3 cm
C Q
R
60° a ⫽ 6 cm
B
S
C
B
Fig. 18.32
A
X
A′
Y
Fig. 18.34
With reference to Fig. 18.32:
With reference to Fig. 18.34:
(i) Draw a line BC, 6 cm long.
(i) Draw a straight line 5 cm long and label it XY . ◦
(ii) Using a protractor centred at C make an angle of 60 to BC. (iii) From C measure a length of 3 cm and label A. (iv) Join B to A by a straight line. Problem 25. Construct a triangle PQR given that QR = 5 cm, ∠Q = 70◦ and ∠R = 44◦ .
(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 .
With reference to Fig. 18.33: Q′
R′
(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).
(iv) The intersection of the arc UV with XC produced, forms the vertex Z of the required triangle. Join YZ by a straight line.
P
Now try the following exercise Exercise 70 70° Q
44° 5 cm
R
Fig. 18.33
Further problems on the construction of triangles (Answers on page 278)
In problems 1 to 5, 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◦
(i) Draw a straight line 5 cm long and label it QR.
3. a = 6 cm, C = 45◦ and B = 75◦
(ii) Use a protractor centred at Q and make an angle of 70◦ . Draw QQ .
4. c = 4 cm, A = 130◦ and C = 15◦
(iii) Use a protractor centred at R and make an angle of 44◦ . Draw RR . (iv) The intersection of QQ and RR forms the vertex P of the triangle. Problem 26. Construct a triangle XYZ given that XY = 5 cm, the hypotenuse YZ = 6.5 cm and ∠X = 90◦ .
5. a = 90 mm, B = 90◦ , hypotenuse = 105 mm