1. The Sine Rule

2. Starter
a) Calculate the Area of an Equilateral triangle with a Perimeter of 30cm (Do this using Trigonometry, not Pythagoras!)
b) What about if the side length was x?

3. The Sine Rule
The Trigonometry we have seen already, involving ‘SOHCAHTOA’ works in Right-angled triangles
There are also some patterns that will work in any triangle
They are called the ‘Sine Rule’ and the ‘Cosine Rule’
Today we will be looking at the Sine Rule, which you are given in the exam booklet

4. The Sine Rule Learning Objectives
All will be able to use the Sine rule to find missing sides in triangles (Grade A)
Most will also be able to use it to find missing angles as well (Grade A)
Some will be able to use it in answering longer questions! (Grade A/A*)

5. The Sine Rule B
Consider the triangle labelled to the right, remembering GCSE trigonometry:
Right hand triangle:
Left hand triangle:
The opposite sides are the same so:
hyp
hyp c a
opp A C
adj b
adj S O H
Divide by c and a 2A

6. The Sine Rule In any triangle: OR a SinA b SinB c SinC = = SinA a
SinBb
SinC c = =

7. The Sine Rule Work out the value of the missing side, labelled ‘a’
a SinA
b SinB
c SinC
Work out the value of the missing side, labelled ‘a’ = =
a Sin74
12 Sin49 =
49° a
12 Sin49
74° a = x
Sin74
12cm a = … a =
15.28 (2dp)

8. The Sine Rule Work out the value of the missing side, labelled ‘y’
a SinA
b SinB
c SinC
Work out the value of the missing side, labelled ‘y’ = =
a Sin101
8.1 Sin38 = a
8.1m
8.1 Sin38 a = x
Sin101
101°
38° a = … a =
12.9 (1dp)

9. The Sine Rule Work out the value of the missing angle, θ. Sinθ 16
SinA a
SinB b
SinC c
Work out the value of the missing angle, θ. = =
Sinθ 16
Sin 76 18 =
18mm
16mm
Sin 76 18
Sinθ = x 16 θ
76°
Sinθ = …
Sin-1 θ =
59.6° (1dp)

10. Plenary a SinA b SinB c SinC = = AB Sin24 17 Sin95 = 17 Sin95 AB = x
6.9409…
6.94

11. Plenary Learning Objectives
All will be able to use the Sine rule to find missing sides in triangles (Grade A)
Most will also be able to use it to find missing angles as well (Grade A)
Some will be able to use it in answering longer questions! (Grade A/A*)

12. Summary We have learnt another rule of Trigonometry, the Sine Rule
We have used it to calculate missing angles and sides in a triangle
We have also seen that it works in any triangle, not just right-angled ones…