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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

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

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:

  • Find h:

2. Find x:

h

x

9


Find x:

x


Find x:

1.

2.

6

x

x


Find x:

x

10


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 = n

HYPOTENUSE = 2 ∙ SHORTER LEG

= 2n

LONGER LEG = SHORTER LEG

= n


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:


Find the missing lengths.

1.

2.

60

g

f

y

x

30

5


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)

b

a

30

45

d

c


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.

60

60


Find the area of the triangle.

45


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