8cm

1
How can we work out the missing angle?
Trigonometry
With trigonometry we can work out
Like Pythagorass Theorem it only works for
right-angled triangles

• An angle given 2 lengths

• A length given an angle and a length

The only thing you have to remember is
In an exam always write this down to remind you
SOH CAH TOA
8cm
5cm
qo
2
Example 1
CAH
SOH
TOA
Sin qo Opposite Hypotenuse
Tan qo Opposite Adjacent
Opposite is always the side opposite the angle
Cos qo Adjacent Hypotenuse
Hypotenuse is always the side opposite the right
angle
We want to work out the angle, what information
have we been given?
SOH CAH TOA
Adjacent is always the side next to the angle
Which ratio has got something to do with an
angle, opposite and hypotenuse
Hypotenuse
Hypotenuse
8cm
8cm
Opposite
Opposite
5cm
5cm
qo
Adjacent
3
Example 1
SOH
Sin qo 0.625
Sin qo Opposite Hypotenuse
Sin-1 Sin qo Sin-1 0.625
The opposite of add is subtract
qo Sin-1 0.625
Sin qo Opposite Hypotenuse
5 cm
The opposite of multiply is divide
8 cm
Substitute in the relevant values
qo 38.68o
The opposite of Sin is Sin-1
You need to find Sin-1 of both sides
Hypotenuse
Hypotenuse
8cm
Opposite
Opposite
5cm
qo
Adjacent
4
Example 2
CAH
SOH
TOA
Sin qo Opposite Hypotenuse
Tan qo Opposite Adjacent
Opposite is always the side opposite the angle
Cos qo Adjacent Hypotenuse
Hypotenuse is always the side opposite the right
angle
We want to work out the angle, what information
have we been given?
SOH CAH TOA
Adjacent is always the side next to the angle
Which ratio has got something to do with an
angle, adjacent and hypotenuse
qo
Hypotenuse
Hypotenuse
5cm
5cm
Adjacent
Adjacent
2cm
2cm
Opposite
5
Example 2
CAH
Cos qo 0.4
Cos-1 Cos qo Cos-1 0.4
The opposite of add is subtract
qo Cos-1 0.4
Cos qo Adjacent Hypotenuse
2 cm
The opposite of multiply is divide
5 cm
Substitute in the relevant values
qo 66.42o
The opposite of Cos is Cos-1
You need to find Cos-1 of both sides
qo
Hypotenuse
Hypotenuse
5cm
Adjacent
Adjacent
2cm
Opposite
6
Example 3
CAH
SOH
TOA
Sin qo Opposite Hypotenuse
Tan qo Opposite Adjacent
Cos qo Adjacent Hypotenuse
In this example we are going to work out the
opposite, what information have we been given?
SOH CAH TOA
Which ratio has got something to do with an
angle, the opposite and the hypotenuse
24o
24o
Hypotenuse
Hypotenuse
5cm
5cm
Angle
Adjacent
Opposite
7
Example 3
Work out the value of Sin 24
SOH
Sin qo Opposite Hypotenuse
Sin 24o Opposite
x 8
x 8
8 cm
Opposite Sin 24o x 8
Sin qo Opposite Hypotenuse
24o
Opposite 0.406737 x 8
To solve this problem we need to rearrange the
formula so that it reads Opposite . In order to
do this we multiply both sides by 8.
Substitute in the relevant values
8 cm
Opposite 3.25
cm
24o
Hypotenuse
Hypotenuse
8cm
Angle
Adjacent
Opposite
8
Your Turn
Use what you have learnt to find the missing
values in each triangle
9m
Use Cos, q 63.61o
a
8cm
qo
Use Sin, a 19.67cm
24o
4m
Use Pythagoras, 15.2mm
a
Use Tan, q 48.81o
Trick
5mm
8cm
qo
16mm
7cm