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IPEKA INTERNATIONAL Christian School Academic Year 2010-2011

Year 9 Mathematics A Teacher: Hedy Lim

The Sine Rule

In trigonometry ratio, we use a right-angled triangle to define the ratio.

QUESTION???

What if the triangle given is not in a right-angled form?

The basic trigonometry ratio SOH CAH TOA can not be used to find the unknown sides or angles.

Supposed we have an acute triangle or an obtuse triangle as given below:

How do we calculate the length of the unknown side or angle? We will use the formula that we are going to call as THE SINE RULE and THE COSINE RULE.

This last two weeks of year 9, we will end up our sub topic only until THE SINE RULE.

opposite hypotenuse

adjacent

Based on the given angle marked , we conclude the sides as adjacent, opposite and hypotenuse

acute obtuse

All three angles in vertices are less than 90o

One angle in one vertex is greater than 90o

Sample

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IPEKA INTERNATIONAL Christian School Academic Year 2010-2011

Year 9 Mathematics A Teacher: Hedy Lim

Remember how to labelling the triangle.

After watching the video, label the triangle PQR below:

Proving the sine rule:

1. Proof by using equation algebra and basic ratio trigonometry: After watching the video, prove by yourself for triangle KLM below with perpendicular height LX :

k

m

l

K

M

L

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IPEKA INTERNATIONAL Christian School Academic Year 2010-2011

Year 9 Mathematics A Teacher: Hedy Lim

2. Proof by Measuring the length of all sides and angles in acute triangle ABC below:

c

b

a

C

B A

A =

B =

C =

a =

b =

c =

Therefore:

sin

sin

sin

aA

bB

cC

=

=

=

sin sin sina b c

A B C= =

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4

IPEKA INTERNATIONAL Christian School Academic Year 2010-2011

Year 9 Mathematics A Teacher: Hedy Lim

Problem Examples using Sine Rule.

After watching the video of one example, do the exercises below:

1. Find the pronumeral.

2. Find the pronumeral.

3. Find the pronumeral.

R Q

P

C

B

A

24 cm

15 cm

280 1050

400

8 cm

g

C

B

A

500

38 cm

56 cm