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Lesson: Trig SOH CAH TOA
Contributed by: Sturges
(Original author: Pappal)
There are 4 things needed to do trigonometry
There are 4 things needed to do trigonometry
1. Trig Formulas
There are 4 things needed to do trigonometry
1. Trig Formulas
2. Labeling Sides
There are 4 things needed to do trigonometry
3. Setting up Formula
1. Trig Formulas
2. Labeling Sides
There are 4 things needed to do trigonometry
3. Setting up Formula
4. Solving Formula
1. Trig Formulas
2. Labeling Sides
4.
There are 4 things needed to do trigonometry
2.
3.
1.
Setting up Formula
?
Solving Formula
?
Trig Formulas
?
Labeling Sides
?
There are SIX trig formulas
There are SIX trig formulas
but we are only going to learn THREE of them.
There are SIX trig formulas
Sine
but we are only going to learn THREE of them.
There are SIX trig formulas
Sine, Cosine
but we are only going to learn THREE of them.
There are SIX trig formulas
Sine, Cosine, Tangent
but we are only going to learn THREE of them.
The formula for sine is
The formula for sine is
Sine ⊾ = 
hypotenuse
opposite
The formula for sine is
The formula for cosine is
Sine ⊾ = 
hypotenuse
opposite
The formula for sine is
The formula for cosine is
Sine ⊾ = 
cosine ⊾ =
hypotenuse
opposite
hyponetuse
adjacent
The formula for tangent is
The formula for sine is
The formula for cosine is
Sine ⊾ = 
cosine ⊾ =
hypotenuse
opposite
hyponetuse
adjacent
The formula for tangent is
The formula for sine is
The formula for cosine is
Sine ⊾ = 
cosine ⊾ =
tangent ⊾ =
hypotenuse
opposite
hyponetuse
adjacent
adjacent
opposite
The formula for tangent is
The formula for sine is
The formula for cosine is
Sine ⊾ = 
cosine ⊾ =
tangent ⊾ =
hypotenuse
?
opposite
hyponetuse
adjacent
?
adjacent
opposite
?
sine ⊾
?
cosine ⊾
?
tangent ⊾
?
=
=
=
adjacent
hypotenuse
opposite
adjacent
opposite
hypotenuse
These formulas can be remember by using
These formulas can be remember by using
SOH
These formulas can be remember by using
SOH
CAH
These formulas can be remember by using
SOH
CAH
TOA
These formulas can be remember by using
S stands for sine
SOH
CAH
TOA
These formulas can be remember by using
C stands for cosine
S stands for sine
SOH
CAH
TOA
These formulas can be remember by using
C stands for cosine
S stands for sine
T stands for tangent
SOH
CAH
TOA
These formulas can be remember by using
C stands for cosine
S stands for sine
T stands for tangent
SOH
CAH
TOA
O stands for opposite
These formulas can be remember by using
C stands for cosine
S stands for sine
T stands for tangent
SOH
CAH
TOA
O stands for opposite
A stands for adjacent
These formulas can be remember by using
C stands for cosine
S stands for sine
T stands for tangent
SOH
CAH
TOA
O stands for opposite
A stands for adjacent
H stands for hypotenuse
Hypotenuse
Opposite
Adjacent
tangent
cosine
sine
Single Letter
Abbreviation
A
?
O
?
C
?
H
?
S
?
T
?
Triple Letter
hyp
?
opp
?
adj
?
tan
?
cos
?
sin
?
Next, you have to be able to label the right triangle.
Next, you have to be able to label the right triangle.
Here are two example triangles
Next, you have to be able to label the right triangle.
Here are two example triangles
Each of these triangles has a right angle
Next, you have to be able to label the right triangle.
Here are two example triangles
Each of these triangles has a right angle
Next, you have to be able to label the right triangle.
and an angle that is marked
Here are two example triangles
Each of these triangles has a right angle
Next, you have to be able to label the right triangle.
and an angle that is marked
Here are two example triangles
The hypotenuse is the side across from the right angle
Next, you have to be able to label the right triangle.
Here are two example triangles
The hypotenuse is the side across from the right angle
Next, you have to be able to label the right triangle.
Here are two example triangles
Hyp
Hyp
The opposite is the side across from the marked angle
The hypotenuse is the side across from the right angle
Next, you have to be able to label the right triangle.
Here are two example triangles
Hyp
Hyp
The opposite is the side across from the marked angle
The hypotenuse is the side across from the right angle
Next, you have to be able to label the right triangle.
Here are two example triangles
Hyp
Opp
Hyp
Opp
The last side is the adjacent
The opposite is the side across from the marked angle
The hypotenuse is the side across from the right angle
Next, you have to be able to label the right triangle.
Here are two example triangles
Hyp
Opp
Adj
Adj
Hyp
Opp
Hyp
?
Opp
?
Adj
Adj
?
Hyp
Opp
Hyp
?
Opp
?
Adj
?
Opposite:
Adjacent:
Hypotenuse:
c
?
a
?
c
b
?
b
a
To figure out which formula to use
you have to look at the sides involved in the problem
To figure out which formula to use
you have to look at the sides involved in the problem
To figure out which formula to use
First, label the sides
35
9
x
you have to look at the sides involved in the problem
To figure out which formula to use
First, label the sides
Hyp
?
35
9
Adj
?
x
Opp
?
you have to look at the sides involved in the problem
To figure out which formula to use
First, label the sides
then determine the sides involved
Hyp
35
9
Adj
x
Opp
you have to look at the sides involved in the problem
To figure out which formula to use
First, label the sides
then determine the sides involved
Hyp
35
9
Adj
x
Opp
we are looking for
This is the side
we are given
you have to look at the sides involved in the problem
To figure out which formula to use
This is the side
First, label the sides
then determine the sides involved
Hyp
35
9
Adj
x
Opp
we are looking for
This is the side
you have to look at the sides involved in the problem
To figure out which formula to use
First, label the sides
then determine the sides involved
so our problem involves Opp and Hyp
Hyp
35
9
Adj
x
Opp
you have to look at the sides involved in the problem
To figure out which formula to use
We will use the formula that has opp and hyp
Hyp
35
9
Adj
x
Opp
you have to look at the sides involved in the problem
To figure out which formula to use
We will use the formula that has opp and hyp
Hyp
SOH CAH TOA
35
9
Adj
x
Opp
you have to look at the sides involved in the problem
To figure out which formula to use
We will use the formula that has opp and hyp
Hyp
SOH CAH TOA
35
9
Adj
x
Opp
you have to look at the sides involved in the problem
To figure out which formula to use
We will use the formula that has opp and hyp
so we will use sine.
Hyp
SOH CAH TOA
35
9
Adj
x
Opp
you have to look at the sides involved in the problem
To figure out which formula to use
sin 35 =
Hyp
35
9
Adj
x
9
x
Opp
sine
cosine
tangent
Which one would I use
15
3
x
20
75
x
sine
cosine
tangent
sine
cosine
tangent
x
77
3
To solve the equation
To solve the equation
you will do different things
To solve the equation
you will do different things
depending on where the x is
To solve the equation
if x is in the top,
you will do different things
depending on where the x is
To solve the equation
if x is in the top,
sin 35 =
you will do different things
depending on where the x is
x
4
To solve the equation
if x is in the top,
sin 35 =
you will do different things
depending on where the x is
x
4
you multiply
To solve the equation
if x is in the top,
sin 35 =
you will do different things
depending on where the x is
x
4
you multiply
4sin35
To solve the equation
If x is in the bottom
you will do different things
depending on where the x is
To solve the equation
If x is in the bottom
sin 35 =
you will do different things
depending on where the x is
x
4
To solve the equation
If x is in the bottom
sin 35 =
you will do different things
depending on where the x is
x
4
you divide
To solve the equation
If x is in the bottom
sin 35 =
you will do different things
depending on where the x is
x
4
you divide
4 / sin 35
To solve the equation
If x is the angle
you will do different things
depending on where the x is
To solve the equation
If x is the angle
you will do different things
sin x =
depending on where the x is
3
4
To solve the equation
If x is the angle
you will do different things
sin x =
depending on where the x is
3
4
you do sin-1
To solve the equation
If x is the angle
you will do different things
sin x =
depending on where the x is
3
4
you do sin-1
sin-1(3/4)
tan 60∘ =
How do you solve?
multiply
divide
tan-1
x
5
sin 45∘ =
How do you solve?
multiply
divide
sin-1
x
5
tan 5∘ =
How do you solve?
multiply
divide
tan-1
10
x
cos 25∘ =
How do you solve?
multiply
divide
cos-1
10
x
cos x∘ =
How do you solve?
multiply
divide
cos-1
10
20
sin x∘ =
How do you solve?
multiply
divide
sin-1
10
20
Label the sides
Hyp
?
Opp
?
x
6
70
Adj
?
Determine which sides are important
Opp & Hyp
Opp & Adj
Adj & Hyp
Hyp
Opp
x
6
70
Adj
Choose the formula
SOH
CAH
TOA
Hyp
Opp
x
6
70
Adj
Fill in the formula
sin
=
Hyp
Opp
6
?
x
?
x
6
70
Adj
How do you solve the problem
sin
=
Hyp
Opp
6
x
x
6
6sin70
6/sin70
sin-1(6/70)
70
Adj
Solve the problem (Round to tenth)
sin
=
Hyp
Opp
6
x
x
6
70
x =
Adj
Label the sides
Opp
?
Hyp
?
9
75
x
Adj
?
Choose the important sides
Opp
Hyp
9
75
x
Opposite & Hypotenuse
Adjacent & Hypotenuse
Opposite & Adjacent
Adj
Choose the correct formula
Opp
Hyp
9
75
x
Adj
SOH
CAH
TOA
Fill in formula
cos
Opp
Hyp
=
9
9
?
x
?
75
x
Adj
Solve Formula
Opp
Hyp
9
75
x
Adj
9cos75
9/cos75
cos-1(9/75)
Solve Formula (Round to tenth)
Opp
Hyp
9
75
x
Adj
Label sides
x
Hyp
?
12
Adj
?
5
Opp
?
Figure out which sides are important
O & H
A & H
O & A
x
Hyp
12
Adj
5
Opp
Find the formula
SOH
CAH
TOA
x
Hyp
12
Adj
5
Opp
Fill in the formula
x
tan
Hyp
=
12
12
?
5
?
Adj
5
Opp
Solve the formula
5tan12
5/tan12
tan-1(5/12)
x
Hyp
12
Adj
5
Opp
Solve the formula (Round to tenth)
x
Hyp
12
Adj
5
Opp
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