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# Sine Rule

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by

## Mr Mattock

on 4 February 2017

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#### Transcript of Sine Rule

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
Examples

Activity