Special Right Triangles

30 60 90 and 45 45 90 Special Right Triangles

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

30 60 90 Right Triangle

Specific Examples

Example 1
example 2

45 45 90 Special Right Triangle

Some Sepcific Examples

Example 1
example 2

Practice Using Special Right Triangles

Problem 1

What is the value of z in the triangle below?

(Don't use the Pythagorean theorem . Use the properties of special right triangles described on this page) problem 1

The 30$$^{\circ}$$ and 60$$^{\circ}$$ angles give this one away. x = 6
2x =12
z = $$ x \sqrt{3} = 6\sqrt{3} $$