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 Special Right Triangles

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:sqrt(3):2. With 2 as the hypotenuse and 1 opposite of the $30^\cic$ (Error compiling LaTeX. Unknown error_msg). That leaves sqrt(3) as the only length left.

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Special Right Triangles

45-45-90 Special Right Triangles

30-60-90 Special Right Triangles

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