**Sine Rule**

Starter

Work out the missing length in the triangle.

What happens to the length if the right angle becomes an acute angle? Or an obtuse angle?

Example

Sine Rule

The ratio of two sides in a non-right triangle is equal to the ratio of the sines of the opposite angles.

**L.O. - Apply the Sine rule to non-right-angled triangles.**

x

27

o

8 cm

Starter

Work out the missing length in the triangle.

What happens to the length if the right angle becomes an acute angle? Or an obtuse angle?

If the right angle becomes acute, x gets smaller.

If the right angle becomes obtuse, x gets bigger.

x

27

o

8 cm

sin 27 =

x =

x = 17.6 cm

8

x

8

sin 27

A

B

a

b

a

sin A

b

sin B

=

Sine Rule

x

23

9.5 cm

6 cm

9.5

sin x

6

sin 23

=

o

o

Sine Rule

Find the size of the missing angle, x, in this triangle.

x

23

9.5 cm

6 cm

o

o

Example

148

6

x

x sin 26

40 sin 6

1.583...

=

sin x

sin 23

0.618...

=

sin x

38.2

=

x

o

=

x

40

= 4.193...

x = 167.75...

h

167.75...

= sin 32

h = 167.75 x sin 32

h = 88.9 m

Activity

Complete the sine rule worksheet

Activity

Complete the sine rule worksheet

Plenary

If you use the values given in the triangles to find the angle opposite side

c

which angle is given, C or C'?

How can you get the other one?

Plenary

If you use the values given in the triangles to find the angle opposite side

c

which angle is given, C or C'?

How can you get the other one?

180 - C = 111.7

It works out C as 68.3

o

o

**Activities**

**Key**

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**Activity**

Answers

Answers

**Worked**

Example

Example

**Worked**

Example

Example

Find the size of the missing angle, x, in this triangle.