*you will be able to find the lengths of sides of special ...€¦ · 30-60-90 right triangle 1 2...

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*You will be able to find the lengths of sides of special

right triangles

45-45-90

And

30-60-90

904545

906030

2:1:1

2:3:1

Leg:Leg:Hypotenuse

Short Leg:Long Leg:Hypotenuse

2:: xxx

xxx 2:3:

In a 45-45-90 triangle…

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

45-45-90 Right Triangle

1

1This is our reference triangle for the 45-45-90.

2

45

45

45-45-90 Right Triangle

x

x

2x

45

45

3

3

x

1

1

3

1

x

EX: 1 Solve for x Let’s set up a proportion by

using our reference triangle.

2

2

3 2x

5

5

x

1

1

5

1

x

2

2

5 2x

EX: 2 Solve for x

x

3

1

1

x

1

3 22

45

EX: 3 Solve for x

x 3

2x

3

2

2

2

x 3 2

2

30-60-90 Right Triangle

1

2

30

60

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

3

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

30-60-90 Right Triangle

x2x

30

60

3x

60

30

x

y

8

x

1

8

2

y 8

23

2 8x

4x

8 3 2y

4 3 y

12

3

30

60

Ex: 1

60

30

x

24

Solve for x

24

2

x

1

12

3

30

60

2x = 24

x = 12

Ex: 2

60

30

x

14

14

2

x

1

12

3

30

60

2x = 14

x = 7

Ex: 3

y

14

2

y

3

2y = 14 3

y = 7 3

60

30

x

x

1

12

3

30

60

x = 5

Ex: 4

y

y

5 3

5 3

3 2

5 3

3

y = 10

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