Basic Engineering Mathematics, Fifth Edition

Angles and triangles 169

Problem 13. Determine angleβin 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 angleθin

Figure 20.8

23  37 

35  49 

A

F

C

B

G

E

D



Figure 20.8

Let a straight lineFGbe drawn throughEsuch thatFG
is parallel toABandCD.
∠BAE=∠AEF(alternate angles between parallel lines
ABandFG), hence∠AEF= 23 ◦ 37 ′.
∠ECD=∠FEC(alternateanglesbetweenparallellines
FGandCD), hence∠FEC= 35 ◦ 49 ′.

Angleθ=∠AEF+∠FEC= 23 ◦ 37 ′+ 35 ◦ 49 ′

= 59 ◦ 26 ′

Problem 15. Determine anglescanddin

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 ◦.

banddare supplementary, henced= 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 ′

Althoughwemaybemorefamiliarwithdegrees,radians

is the SI unit of angular measurement in engineering

(1radian≈ 57. 3 ◦).

(a) Since 180◦=πradthen1◦=

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◦=πradthen1rad=

180 ◦

π

Hence, 0 .743 rad= 0. 743 ×

180 ◦

π

= 42. 57076 ...◦

= 42 ◦ 34 ′

Sinceπ 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

PracticeExercise 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 ◦.