unit 7 part 2 special right triangles 30°, 60,° 90° ∆s 45°, 45,° 90° ∆s

Unit 7 Part 2

Special Right Triangles30°, 60,° 90° ∆s45°, 45,° 90° ∆s

Special Right Triangles

In a 45-45-90 degrees right triangle both legs are congruent and the hypotenuse is the length of the leg times 2

45

45

1

1

45-45-90 Triangle

In a 45-45-90 triangle, the length of the hypotenuse is 2 times the length of one leg.

x

xx

Another way of stating the formula

Example

Determine the length of each side of the following 45-45-90 triangle.

5

45

45

1

1nw

Find the length of each side.

45

45

8 √28 2n

w

45

45

1

1

Find the length of each side.

The hypotenuse is 6 2

45

45

6 2

45

45

1

1

n

w

Find the length of each Variable

This is a 45-45-90 triangle.

x3

y

45

45

1

1

30-60-90 triangle

In a 30-60-90 right triangle this is the format.

3030

30

60

60

60

x 2x

x 1

1

2

2

Hypotenuse = 2

Adjacent to 30 =

Adjacent to 60 = 1

30-60-90 Triangles

In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3 times the length of the shorter leg.

x

x 3

2x

30

60

Another way of stating the formula

Example

Determine the length of each side of the following 30-60-90 triangle.

16

30 30

6012

n

w

Find the length of each variable.

30

60y

x

5 √ 35 3

30

6012

Find the length of each side.

60

30

12n

w

30

60

2

1

Find the length of each variable.

30

60

10

rs

30

6012

30

60 45

45