Cambridge International Mathematics

2 Find the area of a parallelogram with sides 6 : 4 cm and 8 : 7 cm and one interior angle 64 o.

3 If triangle ABC has area 150 cm^2 , find the value ofx.

4 Triangle PQR has PQRb =μ.PQ=10m, QR=12m, and the area of the triangle is 30 m^2.

Find the possible values ofμ.

5 Triangle ABC has AB=13cm and BC=17cm, and its area is 73 : 4 cm^2. Find the measure

of ABC.b

6aFind the area of triangle ABC using:

i angleA ii angleC

b Hence, show that

a

c

=

sinA

sinC

.

Thesine ruleis a set of equations which connects the lengths of the sides of any triangle with the sines of

the opposite angles.

The triangle does not have to be right angled for the sine rule to be used.

THE SINE RULE

In any triangle ABC with sidesa,bandcunits,

and opposite anglesA,BandCrespectively,

sinA

a

=

sinB

b

=

sinC

c

or

a

sinA

=

b

sinB

=

c

sinC

.

Proof: The area of any triangle ABC is given by^12 bcsinA=^12 acsinB=^12 absinC:

Dividing each expression by^12 abcgives

sinA

a

=

sinB

b

=

sinC

c

.

We use thesine rulewhen we are given:

² two sidesand anangle not includedbetween these sides, or

² two anglesand aside.

C THE SINE RULE [8.4]

C

A

B

14 cm

xcm

75°

C

A A

C

B

a

c

b

C

AB

ba

c

GEOMETRY

PACKAGE

The sine rule is used to solve problems involving triangles when angles and sides

opposite those angles are to be related.

Further trigonometry (Chapter 29) 585

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