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Warm Up. 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. 45°-45°-90° Right Triangle.

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Warm Up

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Warm up

Warm Up

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

x

x

7

9

7

9


7 3 special right triangles

7.3: Special Right Triangles

Objectives:

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


45 45 90 right triangle

45°-45°-90° Right Triangle

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 =


Examples

Examples:

  • Find h:

2. Find x:

h

x

9


Warm up

Find x:

x


Find x

Find x:

1.

2.

6

x

x


Find x1

Find x:

x

10


A square has a perimeter of 24 inches how long is the diagonal

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


30 60 90 right triangle

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 = n

HYPOTENUSE = 2 ∙ SHORTER LEG

= 2n

LONGER LEG = SHORTER LEG

= n


If you need to find the shorter leg side opposite 30

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

If given the hypotenuse:

SHORTER LEG =

If given the longer leg:

SHORTER LEG=


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

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


Find the missing lengths

Find the missing lengths.

1.

2.

60

g

f

y

x

30

5


Find the variables

Find the variables.

1.

2.

60

60

x

k

4

m

30

y

30


Find the value of each variable figure not drawn to scale

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

b

a

30

45

d

c


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

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

4

a

45°

b


Find the area round your answer to the nearest tenth

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

60

60


Find the area of the triangle

Find the area of the triangle.

45


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