Basic Engineering Mathematics, Fifth Edition

Angles and triangles 171

20.3 Triangles

Atriangleis a figure enclosed by three straight lines.
The sum of the three angles of a triangle is equal
to 180◦.

20.3.1 Types of triangle

Anacute-angled triangleis one in which all the angles
are acute; i.e., all the angles are less than 90◦.An
example is shown in triangleABCin Figure 20.15(a).
Aright-angled triangleis one which contains a right
angle; i.e., one in which one of the angles is 90◦.An
example is shown in triangleDEFin Figure 20.15(b).

678 598

508

408

548

A

BC

(a) (b)

D

EF

Figure 20.15

Anobtuse-angled triangleis one which contains an
obtuse angle; i.e., one angle which lies between 90◦
and 180◦. An example is shown in trianglePQRin
Figure 20.16(a).
Anequilateral triangleis one inwhich all thesides and
all the angles are equal; i.e., each is 60◦. An example is
shown in triangleABCin Figure 20.16(b).

P

QR

1318

278

22

8

(a)

608

608 608

A

B (b) C

Figure 20.16

Anisosceles triangleis one in which two angles and
two sides are equal. An example is shown in triangle
EFGin Figure 20.17(a).
Ascalene triangleis one with unequal angles and
therefore unequal sides. An example of an acute
angled scalene triangle is shown in triangleABCin
Figure 20.17(b).

(a) (b)

A

B

C

438

828

558

F

E G

308

758 758

Figure 20.17

B

A

C

cb

a



Figure 20.18

With reference to Figure 20.18,

(a) AnglesA,BandCare calledinterior anglesof

the triangle.

(b) Angleθis called anexterior angleof the triangle

and is equal to the sum of the two opposite interior

angles; i.e.,θ=A+C.

(c) a+b+cis called theperimeterof the triangle.

A

C B

b

a

c

Figure 20.19