*You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90

45   45   90 

Leg:Leg:Hypotenuse

1 : 1 : 2

x

:

x

:

x

2 30   60   90  1 : 3 : 2

x

:

x

Short Leg:Long Leg:Hypotenuse

3 : 2

x

In a 45-45-90 triangle…

We will use a reference triangle to set up a proportion then solve.

45-45-90 Right Triangle

45  2 1 45  1

This is our reference triangle for the 45-45-90.

45-45-90 Right Triangle

x

45 

x

2 45 

x

EX: 1 Solve for x 3 3 x Let’s set up a proportion by using our reference triangle.

2

1 3



x

2

x

 3 2

1 1

EX: 2 Solve for x x 5 5 1 5



x

2

x

 5 2

1 1

2

EX: 3 Solve for x 45 3 3

2 

x 1 1 x

x

 3 2

x

 3 2 

x

 3 2 2 2 2

1

2

30-60-90 Right Triangle

60 2 1 30

3

This is our reference triangle for the 30-60-90 triangle.

We will use a reference triangle to set up a proportion then solve.

30-60-90 Right Triangle x

60



x

3

2x 30



Ex: 1

60 x x 1



8 2

x

2

x

  4 8

y 8 1 60 2 30 y



8

3

2

8 3  2

y

3 4 3 

y

30

Ex: 2

30 Solve for x 24 60 x 1 60 2 24



2 x 1 2x = 24 x = 12

3

30

Ex: 3

14 60 14



2 x x 1 2x = 14

x = 7

30 y 1 60 2 14 2

 3

y

3 2y = 14 3

30

y = 7 3

Ex: 4

x 60 y

5 3  3

x 1

x = 5

5 3

30 1 60 2

5 3  3 3

2 y 30

y = 10

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