Special Right Triangles

What kind of triangle is this?Isosceles

What are the measures of the other two angles?

45° and 45°

Find the measure of the missing angles

12 in

12 in

5.3 in

5.3 in

X

X

Find the measure of the missing angles

12 in

12 in

5.3 in

5.3 in

X

X

The missing angles are all

45°

The moral of the story is…

In every isosceles right triangle, • the angles measure 45° - 45° - 90 °

• The two legs are equal in measure

AND… (this is the hard one to remember, but you can do it)

• The hypotenuse is equal to the leg times the square root of 2

X

X

X√245°

45°

Anatomy of a 45° - 45° - 90° triangle

Memorize this picture and learn how to use it!!!!

Find the length of the hypotenuse 12 in

12 in

5.3 in

5.3 in

X

X

Find the length of the hypotenuse 12 in

12 in

5.3 in

5.3 in

X

X

12√2 5.3√2

X√2

Find the length of the missing sides

x

x

8√2 34√2

y√2

45°

Find the length of the missing sides 8

34 34

y

y

8√2 34√2

y√2

45°

8

Find the measure of the missing angles (“theta”)

60°

°

60°

°

°

30 °

Find the measure of the missing angles (“theta”)

60°

° = 30 ° 60°

30° ° = 30 °

° = 60 °

What do you notice about the lengths of the sides?

60°

30 ° 60°

30°30 °

60 °

10 in5 in

44 cm

22 cm

15 cm

7.5 cm

The hypotenuse is twice as long as the side opposite the 30° angle.

30° - 60°- 90° trianglesIn every 30° - 60° - 90° triangle, • the leg opposite the 30 ° angle is the shortest leg

• The hypotenuse is twice as long as the shortest leg

AND… (this is the hard one to remember, but you can do it)

• The middle leg is equal to the shortest leg times the square root of 3

Examples of 30° - 60°- 90° triangles

60°

30 °

60°

30°30 °

60 °

10 in5 in

44 cm

22 cm

15 cm

7.5 cm

The middle length leg is equal to the shortest leg times the square root of 3. It is always opposite the 60° angle.

5√3 in

22√3 cm

15√3 cm

X√3

X

2X30°

60°

Anatomy of a 30° - 60° - 90 ° triangle

Memorize this picture and learn how to use it!!!!