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-

The 30 60 90 Special Right Triangle

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

45 45 90 Special Right Triangle

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