Lesson: Intro Special Right Triangles Public
There are two special types of right triangles:
There are two special types of right triangles:
30  60  90  Triangles
60
30
There are two special types of right triangles:
30  60  90  Triangles
60
30

45  45  90  Triangles

45
45
30
What angles goes here?
45
What angle goes here?
30
45
45
Each of these triangles have their own specific pattern
30
60
Each of these triangles have their own specific pattern
The angle across from the 90 angle equals 2
30
60
Each of these triangles have their own specific pattern
The angle across from the 90 angle equals 2
30
2
60
Each of these triangles have their own specific pattern
The angle across from the 60 angle equals √3
30
2
√3
60
Each of these triangles have their own specific pattern
The angle across from the 30 angle equals 1
30
2
√3
60
1
Match the sides
30
2
?
√3
?
60
1
?
A 45-45-90 triangle also has its own unique pattern
A 45-45-90 triangle also has its own unique pattern
45
45
A 45-45-90 triangle also has its own unique pattern
√2 is opposite of the 90 angle
45
45
A 45-45-90 triangle also has its own unique pattern
√2 is opposite of the 90 angle
45
√2
45
A 45-45-90 triangle also has its own unique pattern
And 1 is opposite both 45 angles
45
√2
45
A 45-45-90 triangle also has its own unique pattern
And x is opposite both 45 angles
45
√2
1
45
1
Match the sides
45
√2
?
1
45
1
?
To solve for one of the sides of a 30-60-90 triangle
you first have to be able to find opposite sides
To solve for one of the sides of a 30-60-90 triangle
you first have to be able to find opposite sides
30

c

a

60

b
doesn't touch the angle
An opposite side
is the side that
To solve for one of the sides of a 30-60-90 triangle
you first have to be able to find opposite sides
Side c
30

c

a

60

b
doesn't touch the angle
An opposite side
is the side that
To solve for one of the sides of a 30-60-90 triangle
Side c
you first have to be able to find opposite sides
Side c
30

c

a

60

b
doesn't touch the angle
An opposite side
is the side that
To solve for one of the sides of a 30-60-90 triangle
Side c
you first have to be able to find opposite sides
Side c doesn't touch the 90 angle
30

c

a

60

b
doesn't touch the angle
An opposite side
is the side that
To solve for one of the sides of a 30-60-90 triangle
Side c
you first have to be able to find opposite sides
Side c doesn't touch the 90 angle
30

c

a

60

b
doesn't touch the angle
An opposite side
90 angle
is the side that
To solve for one of the sides of a 30-60-90 triangle
Side c
you first have to be able to find opposite sides
Side c doesn't touch the 90 angle
so side c is OPPOSITE the 90 angle
30

c

a

60

b
doesn't touch the angle
An opposite side
90 angle
is the side that
30

c

a

60

b
Likewise,
Side a
Side a
30

c

a

60

b
Likewise,
Side a
Side a
30

c

a

60

b
Likewise,
Side a is opposite
the 60 angle
Side a
30
60 angle

c

a

60

b
Likewise,
Side a is opposite
the 60 angle
30
Which side is opposite the 30 angle?

c

a

60

b
side a

side b

side c

side d

30
Which angle is side c opposite from?

c

a

60

b
30

60

90

45

In order to use 30-60-90 triangles
In order to use 30-60-90 triangles
you must be able to match the triangle you are given
In order to use 30-60-90 triangles
you must be able to match the triangle you are given
60
8
x
30
y
In order to use 30-60-90 triangles
you must be able to match the triangle you are given
60
8
with the formula triangle
x
30
y
In order to use 30-60-90 triangles
you must be able to match the triangle you are given
60
8
with the formula triangle
x
30
y
2
60
1
30
√3
In order to use 30-60-90 triangles
you must be able to match the triangle you are given
(2)
60
8
with the formula triangle
x
30
y
2
60
1
30
√3
In order to use 30-60-90 triangles
you must be able to match the triangle you are given
(2)
60
8
with the formula triangle
x
(1)
30
y
2
60
1
30
√3
In order to use 30-60-90 triangles
you must be able to match the triangle you are given
(2)
60
8
with the formula triangle
x
(1)
30
y
(√3)
2
60
1
30
√3
60
(2)
?
(1)
?
30
(√3)
?
2
60
1
30
√3
(1)
?
60
(√3)
?
(2)
?
2
60
1
30
√3
30
Then set up a proportion
(2)
60
8
x
(1)
30
y
(√3)
2
60
1
30
√3
Then set up a proportion
(2)
60
8
x
(1)
30
y
(√3)
2
60
1
30
√3
Then set up a proportion
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
30
√3
parenthesis 
Then set up a proportion
on top
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
30
√3
Then set up a proportion
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
30
√3
Then set up a proportion
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
x
1
30
√3
parenthesis 
Then set up a proportion
on top
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
x
1
30
√3
Then solve the proportion
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
x
1
30
√3
Then solve the proportion
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
x
1
30
√3
2x = 8
Then solve the proportion
(2)
60
8
x
(1)
30
y
(√3)
2
8
=
2
60
1
x
1
30
√3
2x = 8
x =
Put parenthesis on top
7
?
2
?
=
1
?
x
7
60ο
(2)
(1)
x
30ο
(
3
)
Cross Multiply
Put parenthesis on top
7
2
=
2
?
x =
1
x
7
?
7
60ο
(2)
(1)
x
30ο
(
3
)
Cross Multiply
Put parenthesis on top
Solve
7
2
=
2
x = 
x =
1
x
7
7
60ο
(2)
(1)
x
30ο
(
3
)
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