Angles and triangles 169
Problem 13. Determine angle β in Figure 20.7
1338
␣
␤
Figure 20.7
α = 180 ◦ − 133 ◦ = 47 ◦ (i.e. supplementary angles).
α = β = 47
◦ (corresponding angles between parallel
lines).
Problem 14. Determine the value of angle θ in
Figure 20.8
23Њ37Ј
35Њ49Ј
A
F
C
B
G
E
D
␪
Figure 20.8
Let a straight line FG be drawn through E such that FG
is parallel to AB and CD.
∠BAE = ∠AEF (alternate angles between parallel lines
AB and FG), hence ∠AEF = 23 ◦ 37 .
∠ECD = ∠FEC (alternate angles between parallel lines
FG and CD), hence ∠FEC = 35 ◦ 49 .
Angle θ = ∠AEF + ∠FEC = 23
◦ 37
+ 35
◦ 49
= 59
◦ 26
Problem 15. Determine angles c and d in
Figure 20.9
d
b
a
c
468
Figure 20.9
a = b = 46
◦ (corresponding angles between parallel
lines).
Also, b + c + 90 ◦ = 180 ◦ (angles on a straight line).
Hence, 46 ◦ + c + 90 ◦ = 180 ◦ , from which, c = 44
◦ .
b and d are supplementary, hence d = 180 ◦ − 46 ◦
= 134
◦ .
Alternatively, 90 ◦ + c = d (vertically opposite angles).
Problem 16. Convert the following angles to
radians, correct to 3 decimal places.
(a) 73 ◦ (b) 25 ◦ 37
Although we may be more familiar with degrees, radians
is the SI unit of angular measurement in engineering
(1 radian ≈ 57.3 ◦ ).
(a) Since 180
◦
= π rad then 1
◦
=
π
180
rad.
Hence, 73
◦
= 73 ×
π
180
rad = 1.274 rad.
(b) 25 ◦ 37 = 25
37 ◦
60
= 25.616666 ...
Hence, 25
◦ 37
= 25.616666 ...
◦
= 25.616666 ... ×
π
180
rad
= 0.447 rad.
Problem 17. Convert 0.743 rad to degrees and
minutes
Since 180 ◦ = π rad then 1 rad =
180 ◦
π
Hence, 0.743 rad = 0.743 ×
180 ◦
π
= 42.57076 ... ◦
= 42
◦ 34
Since π rad = 180 ◦ , then
π
2
rad = 90 ◦ ,
π
4
rad = 45 ◦ ,
π
3
rad = 60 ◦ and
π
6
rad = 30 ◦
Now try the following Practice Exercise
Practice Exercise 77 Further angular
measurement (answers on page 348)
1. State the general name given to an angle of
197 ◦ .
2. State the general name given to an angle of
136 ◦ .
3. State the general name given to an angle of
49 ◦ .