The 30, 60, 90 Special Right Triangle
The picture below illustrates the general formula for the 30, 60, 90 Triangle.
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.
General Formula
Specific Examples
45, 45, 90 Special Right Triangle
Some Specific Examples
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)
The 30$$^{\circ}$$ and 60$$^{\circ}$$ angles give this one away.
x = 6
2x =12
z = $$ x \sqrt{3} = 6\sqrt{3} $$
