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Warm Up

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

x

x

7

9

7

9

7.3: Special Right Triangles

Objectives:

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

It is an isosceles, right triangle– Both legs are congruent!!

THEOREM:

The hypotenuse is times the length of the legs

IF YOU NEED TO FIND THE HYPOTENUSE:

Hypotenuse = (Length of Leg) X

IF YOU NEED TO FIND A LEG:

Length of leg =

- Find h:

2. Find x:

h

x

9

Find x:

x

1.

2.

6

x

x

x

10

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

Let the shorter leg = n

HYPOTENUSE = 2 ∙ SHORTER LEG

= 2n

LONGER LEG = SHORTER LEG

= n

If given the hypotenuse:

SHORTER LEG =

If given the longer leg:

SHORTER LEG=

1.

2.

60

g

f

y

x

30

5

1.

2.

60

60

x

k

4

m

30

y

30

b

a

30

45

d

c

4

a

45°

b

60

60

45