Difference between revisions of "Special Right Triangles"

Latest revision as of 05:05, 17 November 2022

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.

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 If that is the case, then the [[hypotenuse]] will always be <math>x\sqrt 2</math>.
+==30-60-90 Special Right Triangles==
+-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 <math>30^\circ</math> angle and a <math>60^\circ</math> angle.
+Let's call the side opposite of the <math>30^\circ</math> angle <math>x</math>.
+Then, the side opposite of the <math>60^\circ</math> angle would have a length of <math>x\sqrt 3</math>.
+Finally, the hypotenuse of a 30-60-90 Triangle would have a length of <math>2x</math>.
+There is also the ratio of <math>1:\sqrt3:2</math>. With 2 as the hypotenuse and 1 opposite of the 30 degrees. That leaves <math>\sqrt3</math> as the only length left.
+==See Also==
+[[Pythagorean triple]]