Special Right Triangles

45-45-90 Special Right Triangles

This concept can be used with any right triangle that has two $45^\circ$ angles.

A 45-45-90 Triangle is always isosceles, so let's call both legs of the triangle $x$ .

If that is the case, then the hypotenuse will always be $x\sqrt 2$ .

30-60-90 Triangles are special triangles where there is a certain ratio for the sides of the right triangle, as explained below.

This concept can be used for any right triangle that has a $30^\circ$ angle and a $60^\circ$ angle.

Let's call the side opposite of the $30^\circ$ angle $x$ .

Then, the side opposite of the $60^\circ$ angle would have a length of $x\sqrt 3$ .

Finally, the hypotenuse of a 30-60-90 Triangle would have a length of $2x$ .

There is also the ratio of $1:\sqrt3:2$ . With 2 as the hypotenuse and 1 opposite of the 30 degrees. That leaves $\sqrt3$ as the only length left.