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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 3-
Special Right Triangles Applet
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Right Triangle Calculator
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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))
Answer
The 30° and 60° angles give this one away.
x = 6
2x =12
z = $$x \sqrt{3} = 6\sqrt{3} $$

problem 1