Warm Up

Find the value of x. Leave your answer in simplest radical form.

7 x

9

x

7

9

7.3: Special Right Triangles

Objectives:To use the properties of 45-45-90 and 30-60-90 right triangles

45°-45°-90° Right TriangleIt is an isosceles, right triangle– Both legs are congruent!!

THEOREM:The hypotenuse is times the length of the legs2

IF YOU NEED TO FIND THE HYPOTENUSE: Hypotenuse = (Length of Leg) X

IF YOU NEED TO FIND A LEG:

Length of leg =

2

2

Hypotenuse

Examples:

1. Find h: 2. Find x:

9

h

22

x

Find x:

35x

Find x:

1. 2.

6

x

23x

Find x:

10

x

A square has a perimeter of 24 inches. How long is the diagonal?

30°-60°-90° Right Triangle Shorter Leg is the side opposite the 30° angle Longer leg is the side opposite the 60° angle

Let the shorter leg = nHYPOTENUSE = 2 SHORTER LEG∙

= 2n

LONGER LEG = SHORTER LEG = n

33

If you need to find the shorter leg (side opposite 30°):

If given the hypotenuse:

SHORTER LEG =

If given the longer leg:

SHORTER LEG=

2

Hypotenuse

3

LongerLeg

Fill in the table of values for the side lengths of a 30-60-90 triangle:

Shorter Leg Longer Leg Hypotenuse

3

4

15

34

10

35

32

28

Find the missing lengths.

1. 2. 60

30

g

f

5

xy

6

Find the variables.

1. 2.

30

60

4

x

y

60

30

52

k

m

Find the value of each variable.(Figure not drawn to scale)

b

cd

a

4530

27

Find the value of each variable. Leave your answer in simplest radical form.

23

b

a

4

45°

Find the area. Round your answer to the nearest tenth.

60 60

cm38

Find the area of the triangle.

45

.214 in