Although all right triangles have special features– trigonometric functions and the Pythagorean theorem. The most frequently studied right triangles, the special right triangles, are the 30,60,90 Triangles followed by the 45 45 90 triangles.

### The 30 60 90 Special Right Triangle

The picture below illustrates the general formula for the 30 60 90 Triangle.

#### General Formula

#### Specific Examples

### 45 45 90 Special Right Triangle

#### Some Sepcific Examples

**Practice** Using Special Right Triangles

The 30$$^{\circ}$$ and 60$$^{\circ}$$ angles give this one away.
x = 6

2x =12

z = $$ x \sqrt{3} = 6\sqrt{3} $$