Trigonometric
Ratios
Twitter: @Owen134866
www.mathsfreeresourcelibrary.com
, Prior Knowledge Check
1) Find the unknown values 2) . Sketch the graphs of:
indicated:
a)
a) 3.1cm −𝟑
x 𝟎
23˚
7.3cm b)
x
b)
70˚ 9.05cm −𝟓 −𝟐
8.5cm
c)
c) x 25.8˚
6.2cm
2.7cm −𝟑
d)
d) x
5cm 77.2˚ −𝟔 𝟎
22cm
,Teachings for
Exercise 9A
, Trigonometric Ratios
C
You need to know and be able to use the
Cosine rule to find an unknown side or b a
angle h
We will see where this rule comes from A B
x Xc-x
first!
c
Using Pythagoras’ Theorem in the left triangle, to find length h
Consider the triangle to the right,
labelled using A, B and C, and a, b and c
Replace with the letters
as you are familiar with
used on the diagram
Let us draw on the perpendicular height Using Pythagoras’ Theorem in the right triangle, to find length h
and call it h, down to a point X
Replace with the letters
used on the diagram
This splits side c into two sections
We now have two expressions for h 2. These expressions must
One we will call ‘x’, meaning the other be the same and can therefore be set equal to each other!
section is ‘c – x’
9A
Ratios
Twitter: @Owen134866
www.mathsfreeresourcelibrary.com
, Prior Knowledge Check
1) Find the unknown values 2) . Sketch the graphs of:
indicated:
a)
a) 3.1cm −𝟑
x 𝟎
23˚
7.3cm b)
x
b)
70˚ 9.05cm −𝟓 −𝟐
8.5cm
c)
c) x 25.8˚
6.2cm
2.7cm −𝟑
d)
d) x
5cm 77.2˚ −𝟔 𝟎
22cm
,Teachings for
Exercise 9A
, Trigonometric Ratios
C
You need to know and be able to use the
Cosine rule to find an unknown side or b a
angle h
We will see where this rule comes from A B
x Xc-x
first!
c
Using Pythagoras’ Theorem in the left triangle, to find length h
Consider the triangle to the right,
labelled using A, B and C, and a, b and c
Replace with the letters
as you are familiar with
used on the diagram
Let us draw on the perpendicular height Using Pythagoras’ Theorem in the right triangle, to find length h
and call it h, down to a point X
Replace with the letters
used on the diagram
This splits side c into two sections
We now have two expressions for h 2. These expressions must
One we will call ‘x’, meaning the other be the same and can therefore be set equal to each other!
section is ‘c – x’
9A
